Parking Functions Research Articles

The Urban Park Green Spaces Landscape Premium Functional Value Accounting System: Construction and Application

Urban park green spaces have the functions of improving the urban ecological environment and providing recreational services, and at the same time, they have a certain effect on the value of the surrounding residential property. To quantitatively assess the value of the landscape premium function of park green space, many scholars have carried out research exploration and adopted a variety of methods (such as the contingent valuation method (CVM), travel cost method (TCM) and hedonic price method (HPM)), which have developed from simple theoretical models with single factors to complex empirical models with multiple factors. Among them, the hedonic price method has become the mainstream research method, and in recent years, it has been widely adopted in combination with GIS technology. In terms of research objects, single park green space or multiple park green spaces in large cities are the main focus, while there are fewer studies on park green spaces in built-up areas of small and medium-sized cities. In terms of research content, there are more studies on the value-added coefficient of landscape premium and influence distance, and there are fewer studies on the total value of landscape premium. This article aims to calculate the total landscape premium value of all park green spaces in the built-up areas of small and medium-sized cities, proposing a complete and operable accounting system for the functional value of park green space landscape premiums by combining GIS with a hedonic pricing model and remote sensing image interpretation methods. For the first time, a method for interpreting the height of residential buildings within the benefit range of landscape premium through remote sensing images is proposed, and then the floor area ratio of residential plots is estimated, so as to estimate the total area of actual beneficial buildings. Therefore, this paper takes Chifeng City, a small and medium-sized city, as a case study, and empirically demonstrates the assessment of the landscape premium function of parks and green spaces in the built-up area of Chifeng City by using this accounting system. Research shows that this method has certain feasibility, not only calculating the total value of landscape premium but also addressing the issue in existing studies where all areas within the potential range of landscape premium function are counted as appreciated areas, leading to an overestimation of the premium. It further advances the accuracy of accounting for the value of landscape premium function of urban park green space and provides theoretical reference for the planning and construction of urban park green space.

Classifying Rural Parks: A Case Study in Iowa

Many park professionals use classification systems to simplify complex park spaces into efficient and manageable descriptions. In the United States, the most common classification systems use park size and service area as determinants of a park’s class. While those variables are important in urban spaces, they often fail to capture the unique realities of rural parks. This can lead to misunderstandings, as rural parks are frequently evaluated, programmed, and planned using urbanor-mative assumptions. To address that gap, this paper proposes a new Iowa Rural Park Classification System (IRPCS) that focuses on park function, a crucial de-terminant of rural park use due to the distances between rural destinations. The development of the IRPCS involved collecting data from 749 recreation spaces across an eight-county study area in central Iowa. This data was then analyzed us-ing iterative decision trees to identify, test, and refine the variables that differenti-ate each park class. While ultimately abandoned due to limitations in flexibility, these decision trees played a valuable role in shaping the final park classes.The IRPCS differentiates rural parks from their urban counterparts by highlight-ing the unique variables and characteristics that make them essential utilities. This focus will spark further research and discussions dedicated to rural parks. Additionally, the IRPCS establishes a rural-specific park lexicon, enabling park managers and planners to discuss and analyze rural parks with greater precision.

Interval and $\ell$-interval Rational Parking Functions

Interval parking functions are a generalization of parking functions in which cars have an interval preference for their parking. We generalize this definition to parking functions with $n$ cars and $m\geq n$ parking spots, which we call interval rational parking functions and provide a formula for their enumeration. By specifying an integer parameter $\ell\geq 0$, we then consider the subset of interval rational parking functions in which each car parks at most $\ell$ spots away from their initial preference. We call these $\ell$-interval rational parking functions and provide recursive formulas to enumerate this set for all positive integers $m\geq n$ and $\ell$. We also establish formulas for the number of nondecreasing $\ell$-interval rational parking functions via the outcome map on rational parking functions. We also consider the intersection between $\ell$-interval parking functions and Fubini rankings and show the enumeration of these sets is given by generalized Fibonacci numbers. We conclude by specializing $\ell=1$, and establish that the set of $1$-interval rational parking functions with $n$ cars and $m$ spots are in bijection with the set of barred preferential arrangements of $[n]$ with $m-n$ bars. This readily implies enumerative formulas. Further, in the case where $\ell=1$, we recover the results of Hadaway and Harris that unit interval parking functions are in bijection with the set of Fubini rankings, which are enumerated by the Fubini numbers.

Cost-sharing in Parking Games

In this paper, we study the total displacement statistic of parking functions from the perspective of cooperative game theory. We introduce parking games, which are coalitional cost-sharing games in characteristic function form derived from the total displacement statistic. We show that parking games are supermodular cost-sharing games, indicating that cooperation is difficult (i.e., their core is empty). Next, we study their Shapley value, which formalizes a notion of "fair" cost-sharing and amounts to charging each car for its expected marginal displacement under a random arrival order. Our main contribution is a polynomial-time algorithm to compute the Shapley value of parking games, in contrast with known hardness results on computing the Shapley value of arbitrary games. The algorithm leverages the permutation-invariance of total displacement, combinatorial enumeration, and dynamic programming. We conclude with open questions around an alternative solution concept for supermodular cost-sharing games and connections to other areas in combinatorics.

Research on Optimal Path Planning for Automatic Parking Systems

Abstract The issue of autonomous parking for self-driving vehicles is a critical problem in autonomous driving. With the rapid development of the automotive industry and the increasing number of vehicles, the issues of traffic congestion and parking space shortage have become more prominent, further exacerbating the difficulty of parking. Therefore, there is a growing demand for automatic parking functions. This paper focuses on the problem of self-driving vehicles automatically parking in complex conditions without colliding with other self-driving vehicles and obstacles. The main content includes establishing a vehicle parking kinematic model and solving the minimum turning radius based on the Ackermann vehicle model data. When the self-driving vehicle travels in a straight line, a route from the initial position to the parking space is designed, and an automatic parking model is established. The mathematical model is used to solve the self-driving vehicle’s starting position and end position, as well as the trajectory of the self-driving vehicle, and MATLAB is used to simulate and visualize the parking trajectory. The aim is to solve the problem of parking difficulties caused by factors such as insufficient parking spaces and congested parking scenes. To ensure the safe completion of automatic parking, the path planning algorithm in this paper can plan the optimal parking path.

Sacred sites provide urban green spaces that maintain bird diversity in the megacity of Tokyo, Japan

Green spaces in cities are thought to play an important role in maintaining urban biodiversity. However, it is difficult to create large new areas of green space in big cities. Therefore, existing green spaces need to be conserved and properly managed to conserve urban biodiversity. In big Japanese cities, sacred sites such as shrines, temples, and historic parks are some of the common types of green space. In addition to their role as religious spaces, they may also play an important role in urban biodiversity conservation because of their function as long-term reserves of natural vegetation. In this study, we examined the function of shrines, temples, and historic parks in Bunkyo ward, Tokyo, in maintaining bird diversity by comparing them with urban parks. In addition, a vegetation survey was conducted to identify environmental factors that affect bird diversity, and differences in the bird species observed in each type of green space are discussed. The heterogeneity of bird species composition between study sites was higher among shrines and temples than among urban parks. Forest bird abundance was higher during the breeding season and bird species richness was higher in winter at shrines and temples and historic parks than in urban parks. Bird diversity was positively affected by the abundance of shrubs and evergreen trees. We found that sacred sites were more important than urban parks for maintaining bird diversity. The results also suggested that differences in vegetation structure are a cause of this pattern, and small green spaces in the grounds of sacred sites are managed in a way that is more suitable for maintaining bird diversity. However, shrines and temples, despite their strong historical and cultural value, are threatened by recent urbanization. It is necessary to maintain and properly manage these green spaces as part of urban ecosystems.

Study on the Functions and Design Techniques of Urban Parks in the Context of Post-1949 Urban Development - Case Study of Xian, China

The urban park is an important part of the urban green space system and an essential factor in promoting sustainable development and urban transformation. The functions and corresponding design methods of urban parks also reflect the background and development requirements of different periods. In response to the requirements of urban development in different periods, parks in Xian have gradually changed from a single function of recreation to a function of cultural exchange and, in recent years, to a function of habitat protection. In order to better discuss and analyze characteristics and provide inspiration for further study, the article aims to divide the period from 1949 to 2020 into four stages according to the historical background, and make a comparative analysis according to the corresponding overall planning requirements and examples. The study will combine data with field visits to representative parks from four periods and analyze the relevance of their design and impact to the requirements of the times.The renovation of ancient gardens lays the foundation for the construction of parks, the protection and development of cultural heritage sites increases the role of parks in cultural construction, and the development and construction of ecological wetlands increases the function and role of parks in the construction of ecological civilisation. It can be concluded that the function of the park is also correspondingly related to its design approach.

Results on pattern avoidance in parking functions

Results on pattern avoidance in parking functions

Spatial identification of public spaces’ functions: a case study of Bach Dang Wharf Park in Ho Chi Minh City, Vietnam

Abstract Urban public spaces serve various functions and roles, such as physical, symbolic, ecological, economic, political, social, psychological, and aesthetic. Each function has specific design requirements and holds different meanings for space users. This study aims to identify the location of various functions within Bach Dang Wharf Park, one of the famous central riverside parks of Ho Chi Minh City, Vietnam, and test hypotheses about the concentration of hotspots for each function. To achieve these, we combined participatory GIS methods and face-to-face interviews using quantitative questionnaires and then used SPSS software to examine the relationship between park users’ identification of functions and other factors. We conducted two surveys, each lasting one week, in June 2022 and April 2023, with a total of 223 respondents and 1,413 marked points for park functions. The results showed that how people perceive park functions significantly relates to the characteristics of their park visitation rather than personal information. The hotspots of physical, symbolic, ecological, economic, and political functions appeared with high confidence levels and differed in size and location between the survey times. Meanwhile, in the 2022 survey, hotspots of social function appeared at the old pier near the high-speed boat station and opposite Nguyen Hue walking street. Later in 2023, these areas were mostly concentrated by markers of psychological function. At the same time, hotspots of aesthetic function were recorded in the space in front of the ASEAN flagpole. This approach effectively promotes community involvement in urban planning by better understanding citizens’ needs for public space.

Наукові парки як учасники інноваційних відносин в умовах появи нових соціально-економічних викликів

The article considers science parks as an effective form of participation of higher education institutions and research institutions in innovation relations. The author emphasises that higher education institutions and research institutions are the generators of all innovation processes in society, and therefore the creation of science parks with their participation is an effective platform for the development and implementation of innovations. Science parks are a legal instrument for obtaining funding for the activities of higher education and research institutions. As a result, science parks are legal entities in which society is most interested. Therefore, the author defines science parks as legal entities with special social value. The article emphasises that while for a classical entrepreneurial legal entity the symbiosis of private and public interests characteristic of it is manifested in the dominance of the former, the legal nature of science parks determines the priority of public interests, which is manifested in the functions of a science park established by law. Legislation is based on special legal regulation of science parks which are established and operate in one of the forms of economic partnerships. The article notes the evolution of legal regulation of science parks. The author emphasises that the first version of the special law emphasised public law mechanisms for regulating science parks. The law established an exclusively permissive procedure for the establishment of science parks, a higher education institution or a research institution could be the founder of only one science park, and the form of a science park was not defined. The current version of the special law is marked by changes in the direction of private law approaches to the regulation of science parks. The law clearly defines that science parks are created and operate in the form of business entities, and removes restrictions on the number of science parks that can be created by a higher education institution or research institution. Science parks have become a more universal form of innovation development and implementation. The author concludes that the conceptual approach to the circle of science park founders (higher education institution and/or research institution, other legal entities) and the mechanisms for involving other persons in the implementation of projects by a science park through the institution of partnership is correct. At the same time, the author emphasises the need for certain clarifications of the provisions set out in the special law, which are based on achieving the efficiency of the science park’s implementation of the functions and purpose of its creation.

Research on tourism spatial justice based on residents' perception: A case study on Babao Town of Qilian Mountain National Park (Qinghai area)

As an important nature reserve, national parks play an important role in tourism development, not only in helping residents find employment and maintain vitality, but also in recovering funds, natural education, and environmental protection. Therefore, in the development of national park tourism, it is necessary to adhere to the development concept of spatial justice to ensure the fairness of tourism development. Based on the theory of fairness preference, this paper divides tourism spatial justice into intentional justice, procedural justice, participatory justice, distributive justice, and resultant justice, and discusses the influence relationship between them. Through the questionnaire survey, 241 effective samples are obtained, the structural equation model of tourism spatial justice is constructed, and the path analysis and intermediary effect test are carried out. Research findings: (1) In the tourism spatial justice perception model, procedural justice, participatory justice, and distributive justice all have a significant positive impact on resultant justice, and the path coefficient of distributive justice is the largest. (2) On the path from intentional justice to resultant justice, procedural justice, and participation justice play an intermediary role respectively; Procedural justice and participatory justice, procedural justice and distributive justice play a chain intermediary role respectively. This study divided the dimensions of tourism spatial justice, incorporating participatory justice and distributive justice into traditional equity preference theory, and proved the perception model of tourism spatial justice from the perspective of community residents. At the same time, the interrelationships within the model were verified and explored, exploring the differences between the implementation of tourism spatial justice in national parks and general tourism destinations, to enrich relevant research in the field of tourism spatial justice in national parks and provide reference for the tourism development of national parks. Management implicationsThe development of tourism destinations is pursuing the goal of realizing spatial justice in tourism. The uneven distribution of tourism benefits within national parks is the main reflection of the issue of tourism spatial justice in this study. National park tourism development aims to improve the perception of fairness among local residents and optimize the distribution plan of tourism benefits. The perception of other forms of justice is influenced by the issue of procedural justice among residents. The only way to ensure effective justice in the tourism space within national parks is by ensuring that residents' rights are not compromised in tourism development. In the future, the construction of national parks should attach great importance to considering the distribution and rights of residents, avoiding the problem of residents being able to participate but unable to make profits, in order to better achieve the overall function of national parks.

Analisis Fungsi Taman-Taman Kota di Kota Bogor Berdasarkan Persepsi Masyarakat

The availability of city parks is an important thing in spatial planning. This is regulated in the Ministerial Regulation (Permen) of Public Works (PU) Number 05/PRT/M/2008. Referring to this policy, the number of city parks in Bogor City has met the minimum requirements. However, more than quantity is needed if it is balanced with good quality city parks. This research aims to identify the quality of city park functions in Bogor City based on public perceptions. This research is descriptive with an inductive analysis method. Data was collected from part of the population using a random sampling method. Based on the analysis of the four functions of parks in Bogor City, they are running relatively well. Ecologically, city parks in Bogor, on average, have a good function as noise reducers, oxygen producers, windbreaks, and rain catchment areas. Regarding social and cultural functions, city parks in Bogor City have various assessments. People give a good assessment of the function of city parks as a means of social interaction, recreation, and play. Economically, city parks in the city of Bogor are considered by the community to be a sufficient space for economic interaction. However, no source of products produced from these city parks can have economic value. Aesthetically, city parks in Bogor City have a good average score for their function as supporting the city's beauty, increasing comfort, and forming factors of architectural beauty. It is hoped that the findings from this research can become a basis for improving the arrangement and management of city parks in Bogor City.

Quantitative analysis of social service space equity in urban parks in China

This study aims to quantitatively analyze the equity of social service space in urban parks in China, in order to explore the equity issues faced by different social groups in accessing urban park services. The research background focuses on the importance of urban parks as social service spaces, particularly in improving residents’ quality of life and well-being. Through a comprehensive literature review, the study examines the social service functions of urban parks, the relationship between parks and social psychology, and the theoretical framework of equity. The study employs quantitative research methods, collects data on urban park usage and resident satisfaction, and defines relevant analysis variables. The data analysis section reveals the basic characteristics of park service space usage and resident well-being index through descriptive statistical methods. Subsequently, quantitative analysis is conducted to evaluate the current status of equity in urban park service space and explore the key factors influencing equity. The study reveals a significant correlation between social psychological factors, resident well-being index, and equity in park service space. Finally, the research conclusion emphasizes the importance of improving equity in social service space in urban parks and provides specific policy recommendations. At the same time, the study acknowledges its limitations and suggests future research directions. This study provides insights for urban planners and policymakers on how to enhance equity in urban park services and offers important strategic guidance for improving overall well-being of urban residents.

Higher rank (𝑞,𝑡)-Catalan polynomials, affine Springer fibers, and a finite rational shuffle theorem

We introduce the higher rank ( q , t ) (q,t) -Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a certain standardization map, we define a d i n v \mathtt {dinv} statistic on rank r r semistandard ( m , n ) (m,n) -parking functions and prove c o d i n v \mathtt {codinv} counts the dimension of an affine space in an affine paving of a parabolic affine Springer fiber. Combining these results, we give a finite analogue of the Rational Shuffle Theorem in the context of double affine Hecke algebras. Lastly, we also give a Bizley-type formula for the higher rank Catalan numbers in the non-coprime case.

Research on the Development and Innovative Management Models of Cultural Creative Parks

Under the backdrop of the knowledge economy and globalization, the cultural creative industry, with its unique innovativeness and high added value, has gradually become a new driving force for economic development. Cultural creative parks, as vital platforms for the development of the cultural industry, have aggregated numerous creative enterprises and talents, becoming significant platforms for urban cultural innovation and cultural exchange. The innovation in development and management models of these parks is crucial for enhancing the competitiveness of the cultural industry and promoting urban cultural prosperity. However, with the rapid development of the cultural creative industry, traditional management models can no longer meet the developmental needs of these parks. Therefore, it is imperative to first clarify the functions of cultural creative parks, analyze the factors influencing their development one by one, base strategies on actual conditions, actively explore development and management models, establish market positioning, build on traditional management philosophies with modern management concepts, and strengthen brand building through resource optimization and integration. Implementing these strategies can effectively enhance the operational efficiency and service quality of cultural creative parks, attract more high-quality enterprises and talents, and promote the sustained and healthy development of the parks.

Pendampingan dan Pemenuhan Lampu Panel Surya Sebagai Penerangan Area Taman dalam Konsep Lingkungan Berkelanjutan Bagi Warga

Large and excessive use of electricity, especially for lighting, is also a problem in itself, namely the large expenditure on electricity bills. For this reason, the public is encouraged to use energy-saving lighting such as LED lights or the use of solar panels. Residents want sufficient lighting in public facility areas. Community service activities are carried out at the Babatan Pilang RT Housing Complex. 002 RW. 005, where residents expect assistance from the team to provide education on effective ways to overcome large electricity costs in order to save energy. Apart from that, it will also be realized in the physical form of installing garden lights based on the use of solar panels to remain energy efficient. So that from the results of counseling and fulfillment of garden lights, residents can understand and understand how to save money by getting to know the types of energy-saving lights such as solar panel lights. In terms of park functions, solar panel lights can be shared by residents even if they are used at night.

The Zonotopal Algebra of the Broken Wheel Graph and its Generalization

The machinery of zonotopal algebra is linked with two particular polytopes: the Stanley-Pitman polytope and the regular simplex $\mathfrak{Sim}_n(t_1,...,t_n)$ with parameters $t_1,...,t_n\in \mathbb{R}_+^n$, defined by the inequalities $\sum_{i=1}^n r_i\leq \sum_{i=1}^n t_i, \mbox{ } r_i\in \mathbb{R}_+^n,$ where the $(r_i)_{i\in [n]}$ are variables. Specifically, we will discuss the central Dahmen-Micchelli space of the broken wheel graph $BW_n$ and its dual, the $\mathcal{P}$-central space. We will observe that the $\mathcal{P}$-central space of $BW_n$ is monomial, with a basis given by the $BW_n$-parking functions. We will show that the volume polynomial of the the Stanley-Pitman polytope lies in the central Dahmen-Micchelli space of $BW_n$ and is precisely the polynomial in a particular basis of the central Dahmen-Micchelli space which corresponds to the monomial $t_1t_2\cdots t_n$ in the dual monomial basis of the $\mathcal{P}$-central space. We will then define the generalized broken wheel graph $GBW_n(T)$ for a given rooted tree $T$ on $n$ vertices. For every such tree, we can construct $2^{n-1}$ directed graphs, which we will refer to as generalized broken wheel graphs. Each generalized broken wheel graph constructed from $T$ will give us a polytope, its volume polynomial, and a reference monomial. The $2^{n-1}$ polytopes together give a polyhedral subdivision of $\mathfrak{Sim}_n(t_1,...,t_n)$, their volume polynomials together give a basis for the subspace of homogeneous polynomials of degree $n$ of the corresponding central Dahmen-Micchelli space, and their reference monomials together give a basis for its dual.

Unit Interval Parking Functions and the r-Fubini Numbers

Unit Interval Parking Functions and the r-Fubini Numbers

Adaptive green space management strategies for sustainable carbon sink parks

Green spaces, such as urban parks, function as carbon absorption strategies for the attainment of carbon neutrality. However, urban parks are at risk of losing their carbon absorption function based on changes in carbon flux dynamics due to climate change. Therefore, this study proposes an adaptive green space management strategy for establishing a sustainable carbon sink park by analyzing the carbon flux dynamics of urban parks. To this end, first, a system dynamics model was developed to analyze the carbon flux dynamics of city parks. Second, 10 adaptive green space management programs were established to enable the urban park to function as a carbon sink park. After evaluating the effects of the program, third, three scenarios were built according to the pursued values (ecological, social, economic). As a result of analyzing the carbon flux dynamics, the annual net carbon uptake has continuously decreased since the 2030 s. The amount of carbon uptake has decreased due to a decrease in the rate of photosynthesis, an increase in pests, and mortality. As a result, lawn area decreases, increases in broad-leaf trees, and decreases in lawn management strength were the most effective programs for increasing the carbon uptake by the following order. In addition, the ecological scenario was reported to have the highest cumulative net carbon uptake among the three scenarios. However, all programs and scenarios could not prevent urban parks from losing their carbon sink function. These results presented the flexibility of carbon flux dynamics and how climate change threatened the sustainability of carbon sink parks. According to the results of this study, an adaptive green space management program should be modified to increase carbon sequestration without degrading other functions of urban parks. A further study will be conducted to expand the system dynamics model and analyze the effects of the modified program.

Fixed points of parking functions

We define an action of words in [ m ] n [m]^n on R m {\mathbb {R}}^m to give a new characterization of rational parking functions—they are exactly those words whose action has a fixed point. We use this viewpoint to give a simple definition of Gorsky, Mazin, and Vazirani’s zeta map on rational parking functions when m m and n n are coprime [Trans. Amer. Math. Soc. 368 (2016), pp. 8403–8445], and prove that this zeta map is invertible. A specialization recovers Loehr and Warrington’s sweep map on rational Dyck paths (see D. Armstrong, N. A. Loehr, and G. S. Warrington [Adv. Math. 284 (2015), pp. 159–185; E. Gorsky, M. Mazin, and M. Vazirani [Electron. J. Combin. 24 (2017), p. 29; H. Thomas and N. Williams, Selecta Math. (N.S.) 24 (2018), pp. 2003–2034]).