Parking Functions Research Articles

Assessing Visitors’ Understanding of River National Park Functions and Landscapes

The assessment of visitor understanding and perceptions of natural landscapes and attitudes towards functions of a river national park is important for the acceptance and success of park management. The study asked 426 visitors to the Donau-Auen (Danube Floodplains) National Park in Eastern Austria about their affinity to the national park brand, their understanding of the river landscapes and attitudes towards the functions of a national park, and to what extent the visitors perceive the Danube Floodplains as a national park at all. The results show that a large proportion of respondents have some understanding of river national parks and their functions. Many respondents have a sense of being in a national park. However, for 60% of the respondents, the national park brand played almost no role in a visit to the national park. Visitors who have a higher affinity for the national park showed a stronger agreement with the functions of a national park. Those images from the Danube Floodplains National Park that depicted natural landscapes were judged by the majority of respondents to be typical of a river national park, but also meadows. Differences regarding the national park landscapes were not found among visitor affinity segments. Implications for environmental communication are presented.

Parking functions: interdisciplinary connections

AbstractSuppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If all drivers park successfully, the sequence of choices is called a parking function. Classical parking functions correspond to the case $m=n$ .We investigate various probabilistic properties of a uniform parking function. Through a combinatorial construction termed a parking function multi-shuffle, we give a formula for the law of multiple coordinates in the generic situation $m \lesssim n$ . We further deduce all possible covariances: between two coordinates, between a coordinate and an unattempted spot, and between two unattempted spots. This asymptotic scenario in the generic situation $m \lesssim n$ is in sharp contrast with that of the special situation $m=n$ .A generalization of parking functions called interval parking functions is also studied, in which each driver is willing to park only in a fixed interval of spots. We construct a family of bijections between interval parking functions with n cars and n spots and edge-labeled spanning trees with $n+1$ vertices and a specified root.

Conditional Uniformity and Hawkes Processes

Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, in which exogenously generated initial events give rise to endogenously driven descendant events. This perspective provides the distribution of a cluster’s size through a natural connection to branching processes, but this is irrespective of time. Insight into the chronology of a Hawkes process cluster has been much more elusive. Here, we employ this cluster perspective and a novel adaptation of the random time change theorem to establish an analog of the conditional uniformity property enjoyed by Poisson processes. Conditional on the number of epochs in a cluster, we show that the transformed times are jointly uniform within a particular convex polytope. Furthermore, we find that this polytope leads to a surprising connection between these continuous state clusters and parking functions, discrete objects central in enumerative combinatorics and closely related to Dyck paths on the lattice. In particular, we show that uniformly random parking functions constitute hidden spines within Hawkes process clusters. This yields a decomposition that is valuable both methodologically and practically, which we demonstrate through application to the popular Markovian Hawkes model and proposal of a flexible and efficient simulation algorithm.

On the outcome map of MVP parking functions: Permutations avoiding 321 and 3412, and Motzkin paths

We introduce a new parking procedure called MVP parking in which $n$ cars sequentially enter a one-way street with a preferred parking spot from the $n$ parking spots on the street. If their preferred spot is empty, they park there. Otherwise, they park there and the car parked in that spot is bumped to the next unoccupied spot on the street. If all cars can park under this parking procedure, we say the list of preferences of the $n$ cars is an MVP parking function of length $n$. We show that the set of (classical) parking functions is exactly the set of MVP parking functions although the parking outcome (order in which the cars park) is different under each parking process. Motivating the question: Given a permutation describing the outcome of the MPV parking process, what is the number of MVP parking functions resulting in that given outcome? Our main result establishes a bound for this count which is tight precisely when the permutation describing the parking outcome avoids the patterns 321 and 3412. We then consider special cases of permutations and give closed formulas for the number of MVP parking functions with those outcomes. In particular, we show that the number of MVP parking functions which park in reverse order (that is the permutation describing the outcome is the longest word in $\mathfrak{S}_n$, which does not avoid the pattern 321) is given by the $n$th Motzkin number. We also give families of permutations describing the parking outcome for which the cardinality of the set of cars parking in that order is exponential and others in which it is linear.

Parki dla psów w Warszawie – przestrzenie integracji społecznej czy subtelnej izolacji?

Modern metropolises, such as Warsaw, are dynamically transforming their urban spaces to meet the evolving needs of their residents, both human and animal. One manifestation of these changes is the development of infrastructure dedicated to pets, including dog parks. The aim of this article is to analyze the distribution, accessibility, and functions of dog parks in Warsaw, as well as to assess their role in social integration and potential isolation of users. The field study included the inventory and mapping of 16 parks, as well as in-depth interviews with their users. The results showed that dog parks play a crucial role in the urban ecosystem, contributing to the building of social bonds, although they may be perceived as exclusionary spaces by those who prefer to walk their dogs freely. The article provides valuable insights into the development of pet-friendly urban infrastructure, emphasizing the importance of considering user feedback in the planning and modernization of these spaces.

Positioning and institutional design of the daily management and ecological regulation functions of national parks

Positioning and institutional design of the daily management and ecological regulation functions of national parks

Sociopolitical conflicts on the establishment of protected natural areas: The case of Portofino National Park (Genoa, North-West Italy)

<abstract> <p>This work traces the main stages of environmental and landscape protection of the Portofino Promontory, located in <italic>Riviera Ligure di Levante</italic> (N-W Italy), with particular regard on the recent establishment of Portofino National Park. From 2017, when the institution law was enacted, to date, the park has not yet been established due to the socio-political conflicts that have arisen between some stakeholders and institutions of the territory. These conflicts include not only environmentalists against hunters and constructors but also disagreement between municipalities and region (<italic>Regione Liguria</italic>) and between region and the Ministry of Environment. Today the situation is still stalled, and funds for a park larger than the current one (Portofino Regional Park) have not been allocated. In spite of this, the tug-of-war continues through legal actions. The aim of the article is to analyze the perception of the enlargement of the park by the community and local governance and how this is communicated by the press. The research was conducted through the analysis of the results of a questionnaire aimed at understanding the level of knowledge of the main functions of a national park and the position of the people with respect to it. Second, an analysis of the press was carried out to understand the narratives on this environmental measure. The results of the questionnaire showed a positive consensus toward the park, while press analysis showed little involvement of experts on the subject to foster a political debate without concrete arguments, which damaged the park's image.</p> </abstract>

Utilizing Program of Vacant Land on Public Facilities for Diabetes Mellitus Self-Medication Parks in Benteng Village, Bogor Regency

The prevalence of diabetes in Indonesia has increased substantially in the last 30 years, where individual chances of developing diabetes are higher for women than for men; and level of education is negatively related to diabetes mellitus. Independent therapy garden, is one of the functions of public park which is designed thematically for therapy (medication).The objectives of Program are: (1) Development of a participatory Diabetes Mellitus Self-therapy Garden at partner locations; (2) Cultivation training and education in using/processing of medicinal plants for self-therapy for Diabetes. Program partners are the Kecapi Posyandu RW 6 Benteng Village Bogor Regency, West Java Province. Partner problems are: (1) There are a large number of elderly people who have the potential to suffer from Type 2 Diabetes; (2) Lack of knowledge of partners and residents around partner locations about Diabetes: its characteristics, treatment and prevention; (3) Lack of skills in cultivating and processing of medicinal plants to maintain health, especially diabetes. The participatory approach was carried out by involving partners from the beginning of the program, started from discussing the activity plan, determining the location of the public facility land to be built into a therapy park, and determining program participants. The determination of the location of the park was chosen based on area that was easily visited by residents, so that they can interact with fellow residents in the park. Education about diabetes therapy was carried out by conveying information about diabetes mellitus and how to handle it. Education on the use of medicinal plants, processing them, concocting them, was carried out in practice. There has been an increase in knowledge, skills, and positive attitudes in the prevention and treatment of diabetes independently by partners. The sustainability of the program is carried out by providing diabetes self-therapy manuals, and mentoring through groups through periodic discussions.

Building a New Framework for Urban Parking Facilities Research with Quality Improvement: The Case of Chongqing, China.

People-oriented development has become the main theme of China's current social development, and the construction of various urban infrastructure has shifted from a focus on functionalism to a continuous pursuit of service quality. As an essential infrastructure for urban transport, urban parking facilities have an impact on pedestrian experience and landscape appearance based on the provision of parking functions. Therefore, this study is oriented to improving the quality of parking facilities, proposes a research framework of parking facilities based on meeting functional demand and service quality, and constructs a quality index to evaluate the quality of parking facilities, which includes three dimensions of evaluation indexes: pedestrian space impact, environmental space impact, and demand matching. By analyzing the current characteristics of urban parking facilities and measuring their quality index (6.5), the study finds that while satisfying the basic function of parking demand, it brings a negative impact on the pedestrian experience and the overall urban landscape appearance of the city. Motivated by this, this study proposes strategies to improve the quality of parking facilities: demand matching, spatial synergy, and environmental design to address parking difficulties, while injecting different ideas for future value orientation of parking facility planning and construction.

Some Properties of the Parking Function Poset

In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the framework of finite reflection groups. We present some enumerative and topological properties of this poset. In particular, we get a formula counting certain chains, that encompasses formulas for Whitney numbers (of both kinds). We prove shellability of the poset, and compute its homology as a representation of the symmetric group. We moreover link it with two well-known polytopes : the associahedron and the permutohedron.

FGI를 활용한 민간공원 특례사업 평가항목 선정 연구

This study aims to select evaluation items that can be used in planning park creation to evaluate the proposal to solve the environmental and social problems in promoting private-initiated park development projects. To this end, evaluation items that can consider various aspects of the development project were selected, and the indicators’ validity and appropriateness were carried out through an expert Focus Group Interview (FGI). Firstly, an expert FGI was performed for six major categories and 50 evaluation items derived from literature reviews and brainstorming. As a result, five major and 27 middle category items were selected. Based on the derived major and middle classification items, 95 detailed items were selected. Secondly, 55 sub-items were derived through a suitability questionnaire. As a result of the suitability survey, the average scores of the subcategories for the major categories of natural environment, function of parks, and use of land were relatively high. The average scores for environmental index items such as ecology/vegetation, topography and slope, landscape, park service, wildlife, wide-area ecosystem, and park items were high in the middle classification. The average score of indicators in the natural environment was relatively high, and the average score in the function of parks also soared. In the environmental impact assessment, the occurrence of plan change issues, including the reappraisal of the location, led to unclear detailed evaluation factors for the faithfulness of the plan and the appropriateness of the plan direction. This study is significant in that it is a study on the selection of evaluation items that can minimize the problem of plan alteration and achieve objective evaluation when promoting development projects. This study could be used to forward development projects in the future and evaluate long-term unexecuted urban parks.

Cycle structure of random parking functions

We initiate the study of the cycle structure of uniformly random parking functions. Using the combinatorics of parking completions, we compute the asymptotic expected value of the number of cycles of any fixed length. We obtain an upper bound on the total variation distance between the joint distribution of cycle counts and independent Poisson random variables using a multivariate version of Stein's method via exchangeable pairs. Under a mild condition, the process of cycle counts converges in distribution to a process of independent Poisson random variables.

Konsep Eco Green Park pada Taman Bungkul Surabaya dalam Mewujudkan Environmental Sustainability

<p class="Abstract"><em><span lang="EN-GB">Bungkul Park as one of the green open spaces in Surabaya is known as the best city park locally and internationally. The implementation and management of the park's environment has improved and developed over time. The aim of this paper was to determine whether Bungkul Park Surabaya has been effective in the ecological function of city parks and the application of SDGs to Bungkul Park facilities. The research method used in this study is qualitative by observing the activities of Bungkul Park visitors and conducting literature studies. The results of this paper indicate that Bungkul Park Surabaya needs to apply the concept of a green park to the waste system, structuring street vendors, and landscaping to support the Sustainable Development Goals.</span></em></p>

Residents’ Preferences to Multiple Sound Sources in Urban Park: Integrating Soundscape Measurements and Semantic Differences

Urban parks provide their residents with a space for activities and interactions, and soundscapes play an important role in influencing the residents’ sense of experience of the park environment, with the result that the preferences of residents regarding multiple sound sources can be used as the basis of improving the soundscape quality and optimizing the function of urban parks. Using Shanghai Century Park as the research area, this study focused on the residents’ preference to multiple sound sources based on registered residence differences, and comprehensively used the semantic differential method, importance-performance analysis model, and multinomial logit model to conduct quantitative research on urban park soundscapes and combined the measurement results of the soundscape with the residents’ perception and preference. The results showed that the artificial sounds in Century Park were noisy during the morning and evening peak, while the human sounds were noisy when residents gathered in the park. There was a close relationship between the favorability and subjective loudness of urban park soundscapes, and the residents’ perceptions of urban park soundscapes substantially differed in terms of loudness, tone, and sense of belonging, whereas the differences in the perception of timbre, coverage, and sound source distance were relatively small. Furthermore, it is necessary to enhance the role of natural sounds as well as control the main noise-producing sound sources so that various sounds in the park will not interfere with each other; the optimization of soundscapes should also focus on the residents’ different soundscape preferences due to their individual characteristics.

Generalized bijective maps between G-parking functions, spanning trees, and the Tutte polynomial

We introduce an object called a tree growing sequence (TGS) in an effort to generalize bijective correspondences between G -parking functions, spanning trees, and the set of monomials in the Tutte polynomial of a graph G . A tree growing sequence determines an algorithm which can be applied to a single function, or to the set P G , q of G -parking functions. When the latter is chosen, the algorithm uses splitting operations – inspired by the recursive definition of the Tutte polynomial – to iteratively break P G , q into disjoint subsets. This results in bijective maps τ and ρ from P G , q to the spanning trees of G and Tutte monomials, respectively. We compare the TGS algorithm to Dhar’s algorithm and the family described by Chebikin and Pylyavskyy in 2005. Finally, we compute a Tutte polynomial of a zonotopal tiling using analogous splitting operations.

Hopf algebras of parking functions and decorated planar trees

We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled planar trees extending the Loday-Ronco and Malvenuto-Reutenauer Hopf algebras respectively. We show that the latter is bidendriform which implies that it is also free, cofree, and self-dual. The third algebra involves a new visualization of parking functions as decorated binary trees; it is also bidendriform, free, cofree, and self-dual, and therefore abstractly isomorphic to the algebra PQSym of Novelli and Thibon.We define partial orders on the objects indexing each of these three Hopf algebras, one of which, when restricting to (m+1)-ary trees, coarsens the m-Tamari order of Bergeron and Préville-Ratelle. We show that multiplication of dual fundamental basis elements is given by intervals in each of these orders.Finally, we use an axiomatized version of the techniques of Aguiar and Sottile on the Malvenuto-Reutenauer Hopf algebra to define a monomial basis on each of our Hopf algebras, and to show that comultiplication is cofree on the monomial elements. This in particular, implies the cofreeness of the Hopf algebra on planar trees. We also find explicit positive formulas for the multiplication on monomial basis and a cancellation-free and grouping-free formula for the antipode of monomial elements.

The Park city perspective study: Revealing the park accessibility influenced by experiences of visitors under different travel modes

With social media platforms becoming popular in recent years, Big Data has become an effective way to explore human-oriented service capability of parks. In this research, the spatial accessibility of urban parks under four different travel modes (driving, transiting, biking, and walking) and multiple modes was analyzed by integrating the actual experiences of visitors and real travel time. We took the built-up area of Chengdu, Sichuan Province, China as the research area and drew conclusions as follows: 1) park accessibility of Chengdu still has a large space for promotion. 2) Residents living in the east region of Qingyang District and Wuhou District, north area of Jinniu District, and Chenghua District are more convenient to visit parks, as well as the population center of Longquanyi District, Shuangliu District, and Pidu District. In addition, riders and walkers are more likely to go to the nearest park. 3) Accessibility of parks would be affected significantly during peak hours and weekends by driving and multiple modes, while the other travel modes had little influence. 4) Spatial aggregation was more obvious during the peak hours of weekdays under driving modes, while there were obvious cold spot areas distributed continuously for riders. 5) Park desert was found in Yongquan Subdistrict, Jitouqiao Subdistrict, and Chenglonglu Subdistrict, which were near the downtown. Overall, Chengdu must make rational use of small and micro spaces in the city to add greenery to the corners of the city and integrate parks with other surrounding industries to inspire the entertainment, economy, and tourism function of parks. Through the modified 2SFCA method, this study provide a more realistic and human-oriented way to demonstrate the accessibility. Also, the results can guide cities to understand what reasonable and appropriate parks they need to build to achieve the equalization of park recreation services.

Spatiotemporal Study of Park Sentiments at Metropolitan Scale Using Multiple Social Media Data

Creating wonderful emotional experiences is the critical social function and cultural service of urban parks. Park sentiment patterns in rapidly urbanizing metropolitan areas need to be understood and interpreted thoroughly. This research aims to systematically study park sentiment patterns in metropolitan areas. By focusing on parks in Shanghai city and using the local mainstream social media data (SMD) of Dazhong Dianping, Ctrip, and Weibo, we created a series of score-related indicators to estimate park sentiment. We then applied statistical analyses to systematically interpret sentiment patterns in the spatial, temporal, and spatiotemporal domains, explored their related factors, and compared the performance of different SMD sources. The results proved that Shanghai parks generally bring positive emotions to visitors but showed uneven sentiment patterns citywide. Park sentiment distributions differed from various SMD sources, but the SMD sets of Dazhong Dianping and Ctrip showed significant correlations. For these two SMD sets, visitors have greater and more stable happiness in parks on a workday than on a non-workday and in spring than in other seasons. Parks with higher positive sentiments are scattered citywide, whereas those with lower emotions are clustered in the downtown area. For Weibo, more positive emotions occurred on non-workdays or in autumn, and the lower mood clustering did not exist. Moreover, the quality-related internal factors of the park itself, rather than external factors such as location and conditions, were identified to influence park sentiment. The innovations of park sentiment methods in this study included using multiple SMD sets, creating more accurate sentiment indexes, and applying statistics in temporal, spatial, and spatiotemporal domains. These enhanced sentiment analyses for urban parks to obtain more systematic, comprehensive, and thorough results. The defects and improvements for urban park construction were explored by interpreting park sentiment patterns and possible causes and effects. This motivates better park management and urban development, and enlightens urban planners, landscape designers, and policymakers.

Generalizing Parking Functions with Randomness

Consider $n$ cars $C_1, C_2, \ldots, C_n$ that want to park in a parking lot with parking spaces $1,2,\ldots,n$ that appear in order. Each car $C_i$ has a parking preference $\alpha_i \in \{1,2,\ldots,n\}$. The cars appear in order, if their preferred parking spot is not taken, they take it, if the parking spot is taken, they move forward until they find an empty spot. If they do not find an empty spot, they do not park. An $n$-tuple $(\alpha_1, \alpha_2, \ldots, \alpha_n)$ is said to be a parking function, if this list of preferences allows every car to park under this algorithm. For an integer $k$, we say that an $n$-tuple is a $k$-Naples parking function if the cars can park with the modified algorithm, where when car $C_i$'s preference is taken, $C_i$ backs up $k$-spaces (one by one) and takes the first empty spot. If there are no empty spots in the (up to) $k$ spaces behind $\alpha_i$, they then try to find a parking spot in front of them. We introduce randomness to this problem in two ways: 1) For the original parking function definition, for each car $C_i$ that has their preference taken, we decide with probability $p$ whether $C_i$ moves forwards or backwards when their preferred spot is taken; 2) For the $k$-Naples definition, for each car $C_i$ that has their preference taken, we decide with probability $p$ whether $C_i$ backs up $k$ spaces or not before moving forward. In each of these models, for an $n$-tuple $\alpha\in\{1,2,\ldots,n\}^n$, there is now a probability that the model ends in all cars parking or not. For each of these random models, we find a formula for the expected value. Furthermore, for the second random model, in the case $k =1$, $p=1/2$, we prove that for any $1\le t\le 2^{n-2}$, there is exactly one $\alpha\in\{1,2,\ldots,n\}^n$ such that the probability that $\alpha$ parks is $(2t-1)/2^{n-1}$.

Maximal Chains in Bond Lattices

Let $G$ be a graph with vertex set $\{1,2,\ldots,n\}$. Its bond lattice, $BL(G)$, is a sublattice of the set partition lattice. The elements of $BL(G)$ are the set partitions whose blocks induce connected subgraphs of $G$.
 In this article, we consider graphs $G$ whose bond lattice consists only of noncrossing partitions. We define a family of graphs, called triangulation graphs, with this property and show that any two produce isomorphic bond lattices. We then look at the enumeration of the maximal chains in the bond lattices of triangulation graphs. Stanley's map from maximal chains in the noncrossing partition lattice to parking functions was our motivation. We find the restriction of his map to the bond lattice of certain subgraphs of triangulation graphs. Finally, we show the number of maximal chains in the bond lattice of a triangulation graph is the number of ordered cycle decompositions.