Parking Functions Research Articles

Legibility of neighborhood parks as a predicator for enhanced social interaction towards social sustainability

Researchers commonly acknowledge the functions of neighborhood parks in terms of social interaction and their potential roles as social integrators. Nevertheless, many cities are facing the problem of underutilized parks which could be due to the park elements that are not legible and appealing. This paper examines the relationship between legibility attributes (clear structure, visual obstacles, and accessibility) with social interaction (park engagement and the intensity of contact) within neighborhood parks. To confirm the extent to which legibility attributes predict social interaction, surveys were conducted with 378 participants in the neighborhoods of Putrajaya, Malaysia. Results revealed that legibility of the neighborhood parks influences duration of use, which in turn increases the potential for social interactions among neighborhood residents. The level of visual obstruction was strongly linked with the quality of the edges and distances between park activities. The findings highlight the importance of legibility in the planning and design of public spaces to encourage residents to stay longer while enhancing interaction in neighborhood parks and ultimately achieving social sustainability.

Bounded height interlaced pairs of parking functions

We enumerate interlaced pairs of parking functions whose underlying Dyck path has a bounded height. We obtain an explicit formula for this enumeration in the form of a quotient of analogs of Chebyshev polynomials having coefficients in the ring of symmetric functions.

A weighted sum over generalized Tesler matrices

We generalize previous definitions of Tesler matrices to allow negative matrix entries and negative hook sums. Our main result is an algebraic interpretation of a certain weighted sum over these matrices, which we call the Tesler function. Our interpretation uses a new class of symmetric function specializations which are defined by their values on Macdonald polynomials. As a result of this interpretation, we obtain a Tesler function expression for the Hall inner product $$\langle \Delta _f e_n, p_{1^{n}}\rangle $$ , where $$\Delta _f$$ is the delta operator introduced by Bergeron, Garsia, Haiman, and Tesler. We also provide simple formulas for various special cases of Tesler functions which involve q, t-binomial coefficients, ordered set partitions, and parking functions. These formulas prove two cases of the recent Delta Conjecture posed by Haglund, Remmel, and the author.

Evaluation and Optimization of Models' Priorities in Redesigning of Urban Parks in Semi-Mountainous Areas

With the growing trend for semi-natural spaces in urban areas, urban parks and the related social behaviors have been faced with more interest. However, the flaw in the original design, changes in the park field and variation in living standards level of users, causes situation that lead to some inappropriate performance functions of the parks or parks unable to provide optimal quality of these functions. The main objective of this study was to address these failings and to advance the cause, using problem solving method proposed in this social-architectural research. In this context, semi-mountainous areas parks, review as case studies due to the nature of subject and locating in the particular region in the country for evaluation the priority of redesigning principles.To achieve this goal, redesigning in urban parks is defined and after studying worldwide experience and situation analysis, by using a qualitative evaluation in an urban park in Khoram-Abad, Arak and Hamadan, redesigning principles is proposed. The research method was descriptive-analytical and information collecting method have been taken by theoretical studies through library method and field studies including survey of the physical condition of the park and picked up a case study and statistical distribution of questionnaires among 224 presented persons in the park. The statistical analysis was performed on the responses of consumers by analysis program R and the frequency response is obtained. To assess the principles' priority of redesigning in the city's parks, the covariance was used.The results show that the three principles: consideration to the union, linkage and coordination between the initial layout and redesigning plan of parks, optimizing the ecological functions of Park and optimizing social functions of Park through the relevant mechanisms should be in interest and commitment in redesigning parks of semi-mountainous areas.

Certain variants of multipermutohedron ideals

Multipermutohedron ideals have rich combinatorial properties. An explicit combinatorial formula for the multigraded Betti numbers of a multipermutohedron ideal and their Alexander duals are known. Also, the dimension of the Artinian quotient of an Alexander dual of a multipermutohedron ideal is the number of generalized parking functions. In this paper, monomial ideals which are certain variants of multipermutohedron ideals are studied. Multigraded Betti numbers of these variant monomial ideals and their Alexander duals are obtained. Further, many interesting combinatorial properties of multipermutohedron ideals are extended to these variant monomial ideals.

Objective influencing factors of urban park accessibility

Urban park accessibility is an important indicator to measure the level of urban modern development, and the harmonious relationships between people and land. It is meaningful for efficiently increasing urban park accessibility, fully providing services functions of urban park and promoting healthy development of cities to understand objective influencing factors of urban park accessibility and its extent of impact. The service area and service efficiency of urban parks in three-ring area of Shenyang City were evaluated basing on ArcGIS 9.3 software platform and network analysis methods. The regularity of the service area and service efficiency of urban parks changing with the urban park area, urban park shape and road network density were analyzed. The results showed that urban park area had significant positive correlation with service area and significant negative correlation with service efficiency. Urban park shape had significant positive correlation with service area and service efficiency. Road network density had significant negative correlation with service area of urban parks, but had no significant correlation with service efficiency. Based on the extent of impact on urban park service area, the importance of three influencing factors was in the order of urban park area> road network density > urban park shape. Based on the extent of impact on urban park service efficiency, the importance of three influencing factors was in the order of urban park area> urban park shape > road network density. Urban park area was the most important influencing factor for the service area and service efficiency of urban parks.

A Decomposition of Parking Functions by Undesired Spaces

There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of the corresponding maximal chains. We introduce a decomposition of parking functions based on the largest number omitted and prove several theorems about the corresponding posets. In particular, they share properties with the noncrossing partition lattice such as local self-duality, a nice characterization of intervals, a readily computable Möbius function, and a symmetric chain decomposition. We also explore connections with order complexes, labeled Dyck paths, and rooted forests.

The Number of Prefixes of Minimal Factorisations of a Cycle

We prove in two different ways that the number of distinct prefixes of length $k$ of minimal factorisations of the $n$-cycle $(1\ldots n)$ as a product of $n-1$ transpositions is $\binom{n}{k+1}n^{k-1}$. Our first proof is not bijective but makes use of a correspondence between minimal factorisations and Cayley trees. The second proof consists of establishing a bijection between the set which we want to enumerate and the set of parking functions of a certain kind, which can be counted by a standard conjugation argument.

Parking functions and tree inversions revisited

Kreweras proved that the reversed sum enumerator for parking functions of length n is equal to the inversion enumerator for labeled trees on n+1 vertices. Recently, Perkinson, Yang, and Yu gave a bijective proof of this equality that moreover generalizes to graphical parking functions. Using a depth-first search variant of Dhar's burning algorithm they proved that the reversed sum enumerator for G-parking functions equals the κ-number enumerator for spanning trees of G. The κ-number is a kind of generalized tree inversion number originally defined by Gessel. We extend the work of Perkinson–Yang–Yu to what are referred to as “generalized parking functions” in the literature, but which we prefer to call vector parking functions because they depend on a choice of vector x∈Nn. Specifically, we give an expression for the reversed sum enumerator for x-parking functions in terms of inversions in rooted plane trees with respect to certain admissible vertex orders. Along the way we clarify the relationship between graphical and vector parking functions.

국내 역사공원의 지정 및 조성 경향 분석

2005년 도시공원법 개정 이후 국내에는 역사유산의 보전은 물론 도시민의 휴식과 교육을 함께 도모할 수 있는 역사공원이 등장하였다. 이제는 역사공원의 운영 실태를 통해 국내 역사공원의 특성을 알고 그에 따른 제도적 보완을 모색할 때이다. 본 연구는 주요 국가의 역사공원 제도의 특성과 국내 역사공원의 지정 및 조성 경향을 분석하여 역사공원의 기능과 역할을 점검하고 향후 대응 방향을 마련하고자 하였다. 연구는 문헌고찰을 중심으로 하되, 역사공원 현황과 조성 과정을 관계 공무원과 전문가에게 전화 및 이메일로 확인하였다. 연구 결과, 역사자원은 주로 조선시대 유적에 집중되어 있지만 인물, 사건, 장소 등의 유산도 포함되며 근대기 유산도 증가하는 추세를 보였다. 역사공원은 기존도시와 신도시, 대도시와 지방도시 사이에 차이가 있으며 지방도시는 최근 경제 활성화와 정체성 강화를 위한 중요한 자원으로 역사공원을 이용하는 경향을 보였다. 또한, 공원의 종류를 역사공원으로 변경한 경우, 기존 기능과 일부 상충하는 문제가 발생하였다. 국내 역사공원은 역사유산공원, 역사기념공원, 역사주제공원과 역사적공원의 네 가지 유형으로 구분할 수 있었다. 이러한 세부적 유형분류는 향후 역사유산의 보전과 활용을 위한 전략적 토대가 되며 역사공원의 구체적인 운영 방향을 제시하는 기준이 될 수 있다. After the revision of the Urban Park Act in 2005, historical parks emerged in Korea to promote the preservation of historical heritage while also offering recreation and education to ordinary citizens. It is now time to examine the characteristics of domestic historical parks by examining their current operational conditions, and seek appropriate institutional improvements. By studying the characteristics of historical parks in various countries, as well as the trends in the designation and development of domestic historical parks, this study attempts to examine the function and role of historical parks, and seeks a direction for future action. Through its literature review, this study also examines the current state of historical parks through cooperation with relevant public officials and experts. The results of the study show that, despite historical resources being concentrated in sites dating to the Joseon Dynasty, they also include heritage pertaining to persons, events, and places. There is also a trend toward increasing the focus on modern heritage. Historical parks show differences across existing cities and new towns, as well as between major cities and provincial cities. Provincial cities showed a recent trend of using historical parks as important resources for strengthening their economics and solidifying their identities. Also, there are many cases where the designated category for a park is changed to a historical park. In such cases, there may be a problem where certain functions of the park run into conflict. Domestic historical parks can be divided into four categories: heritage parks, memorial parks, historical theme parks, and historic parks. Such detailed classification schemes may serve as the strategic foundation for later conservation and usage of historical heritage, as well as a standard for suggesting concrete direction in the operation of historical parks.

Cyclic Sieving and Rational Catalan Theory

Let $a < b$ be coprime positive integers. Armstrong, Rhoades, and Williams (2013) defined a set NC(a,b) of `rational noncrossing partitions', which form a subset of the ordinary noncrossing partitions of $\{1, 2, \dots, b-1\}$. Confirming a conjecture of Armstrong et. al., we prove that NC(a,b) is closed under rotation and prove an instance of the cyclic sieving phenomenon for this rotational action. We also define a rational generalization of the $\mathfrak{S}_a$-noncrossing parking functions of Armstrong, Reiner, and Rhoades.

Parking functions for mappings

We apply the concept of parking functions to functional digraphs of mappings by considering the nodes as parking spaces and the directed edges as one-way streets: Each driver has a preferred parking space and starting with this node he follows the edges in the graph until he either finds a free parking space or all reachable parking spaces are occupied. If all drivers are successful we speak of a parking function for the mapping. We transfer well-known characterizations of parking functions to mappings. Via analytic combinatorics techniques we study the total number Mn,m of mapping parking functions, i.e., the number of pairs (f,s) with f:[n]→[n] an n-mapping and s∈[n]m a parking function for f with m drivers, yielding exact and asymptotic results. Moreover, we describe the phase change behaviour appearing at m=n/2 for Mn,m and relate it to previously studied combinatorial contexts.

Rational parking functions and LLT polynomials

We prove that the combinatorial side of the “Rational Shuffle Conjecture” provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT polynomial, thus generalizing the result of Haglund, Haiman, Loehr, Remmel and Ulyanov. The corresponding skew diagram is described explicitly in terms of a certain (m,n)-core.

Drivers of biodiversity patterns in parks of a growing South American megacity

How urban habitats contribute to biodiversity conservation is a key challenge in a rapidly urbanising world. Urban parks can provide important habitats for native species, but previous studies are geographically biased; fast growing megacities, in particular in South America, are clearly understudied. To assess habitat functions and underlying drivers in parks of Santiago de Chile, we analysed the assemblages of wild growing plant species in two ubiquitous park habitat types (grasslands, wooded areas) in 15 parks (150 plots) along an urban-rural gradient. We first used linear contrasts to compare species richness, beta diversity and the proportion of introduced species. We then tested for the explanatory value of environmental variables operating at different spatial scales (plot, park, urban matrix). Unlike in most previous studies, biodiversity patterns were not related to the position of the parks on the urban-rural gradient. Introduced species, mostly from Europe, generally dominated both habitat types (>90 %). Socio-economic (population growth or density), but not spatial, variables were retained in most models. Maintenance intensity was most influential in predicting species assemblages, complemented by park age in wooded areas. A high proportion of European grassland species indicates a trend of homogenisation in park grassland at a cross-continental scale. We conclude that habitat functions of urban parks for native species that have been mainly demonstrated for Europe cannot be generalised to South American megacities. This highlights the need for innovative and locally appropriate conservation approaches (e.g., re-introduction of native species) to foster biodiversity functions in urban parks of South American megacities.

Affine permutations and rational slope parking functions

We introduce a new approach to the enumeration of rational slope parking functions with respect to the area \operatorname {area} and a generalized dinv \operatorname {dinv} statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to two previously known combinatorial constructions: Haglund’s bijection ζ \zeta exchanging the pairs of statistics ( area , dinv ) (\operatorname {area},\operatorname {dinv}) and ( bounce , area ) (\operatorname {bounce}, \operatorname {area}) on Dyck paths, and the Pak-Stanley labeling of the regions of k k -Shi hyperplane arrangements by k k -parking functions. Essentially, our approach can be viewed as a generalization and a unification of these two constructions. We also relate our combinatorial constructions to representation theory. We derive new formulas for the Poincaré polynomials of certain affine Springer fibers and describe a connection to the theory of finite-dimensional representations of DAHA and non-symmetric Macdonald polynomials.

Triumph of parks: how socio-economic dynamics change urban green

This paper explores the current paradigm shift regarding the use, function and design of city parks in Amsterdam. Looking back in history, city parks are relatively new phenomena within the urban tissue. Dating from the late eighteenth century, they announced a completely new kind of public realm within cities. During the 1920s a novel type of park came into being in Germany, which put its mark on Dutch parks designed after World War II. Today parks have again changed character. On the basis of the results of Het Grote Groenonderzoek 2013 (the Great Green Survey) of the municipality of Amsterdam, this change can be quantified and qualified. Moreover, specific trends and tendencies can be distinguished. In fact, ‘street photography’ and a design analysis of Amsterdam's current parks have confirmed these results as well. Recent designs for Flevopark and Parool Triangle are examples of how ‘designing with green’ can contribute in an inspiring way to ongoing and future urban transformations. Finally, this paper tries to reflect on the transformation from an industrial-service economy towards a knowledge-based economy, where the quality of green public space in the urban fabric is a decisive location factor for knowledge workers and businesses.

EVALUASI FUNGSI EKOLOGIS RUANG TERBUKA HIJAU (RTH) PERKOTAAN SEBAGAI AREAL RESAPAN DI KOTA PONTIANAK (STUDI KASUS: TAMAN ALUN KAPUAS)

ABSTRACTAlun Kapuas Park is a city park that designated by The Park Departement as Green Open Space (RTH) in Pontianak city. In connection with the function of RTH as rainwater catchment, Alun Kapuas Park still got less attention because puddle often happens during the rainy season. This research aims to determine 1) infiltration rate when the condition is not raining and the day condition is raining, 2) the influence of soil physical characteristic and vegetation against the infiltration rate, 3) the potential of Alun Kapuas Park to absorb rainwater. Infiltration rate measurement method uses double ring infiltrometer, then it is analyzed by the method of Horton. The result of research indicate that the condition of dry day has average infiltration rate value of 5,62 cm/h greater than the condition of rainy days has average infiltration rate value of 3,20 cm/h. The highest infiltration rate value of 14,40 cm/h is point 4 with sand soil value of 64,64%, permeability value of 26,29 cm/h, and porosity value of 55,42%. Lowest infiltration rate value of 2,02 cm/h is point 3, with sand soil value of 54,41%, permeability value of 5,14 cm/h, and porosity value of 47,33%. The greater values of permeability, porosity, and the sand fraction can increase the infiltration rate. Vegetation at Point 1, Point 2 and Point 4 is dominated by trees and grass have infiltration rate greater than 3 points dominated the ground cover plants and shrubs. Potential seepage of rain for one year in Alun Kapuas Park is 37% of the total volume of rainfall amounted to 54.801 m3, so it does not fulfill the ecological functions of city park as rainwater catchment have percentage of 75-95%. Something that can be suggested is expanding the area of reforestation, choosing the composition of the vegetation right, replacing asphalt with paving blocks, and social-economic activities are not carried out in the area of reforestation.Key word: city park , infiltration rate, soil physical characteristic, vegetation

Optimize the Use of a Parking Space in a Residential Area

Development of a multi-storey building is gaining popularity in modern conditions; however, the designers do not pay enough attention to the organization of the parking space. This leads to a chaotic “parking function” machines in intrayard territories. Cars are on the lawns, playgrounds and intradomestic driveways forming traffic congestion for special service cars.It can be noted in the result of analysis that different types of parking in residential complexes widely used both abroad and in Russia, in particular, there is a tendency to introduce the practice of mechanized and combined (ramp and mechanized) parking (underground and surface).Objective: to optimize the organization of a parking space in a congested residential area on the criterion of maximizing the use of intrayard space.

On moment sequences and mixed Poisson distributions

In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable (X) with moment sequence ((mu_s)_{sinmathbb{N}}) we determine a discrete random variable (Y), whose moment sequence is given by the Stirling transform of the sequence ((mu_s)_{sinmathbb{N}}), and identify the distribution as a mixed Poisson distribution. We discuss properties of this family of distributions and present a new simple limit theorem based on expansions of factorial moments instead of power moments. Moreover, we present several examples of mixed Poisson distributions in the analysis of random discrete structures, unifying and extending earlier results. We also add several entirely new results: we analyse triangular urn models, where the initial configuration or the dimension of the urn is not fixed, but may depend on the discrete time (n). We discuss the branching structure of plane recursive trees and its relation to table sizes in the Chinese restaurant process. Furthermore, we discuss root isolation procedures in Cayley trees, a parameter in parking functions, zero contacts in lattice paths consisting of bridges, and a parameter related to cyclic points and trees in graphs of random mappings, all leading to mixed Poisson-Rayleigh distributions. Finally, we indicate how mixed Poisson distributions naturally arise in the critical composition scheme of Analytic Combinatorics. <script type=text/javascript src=//cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML>

G-parking functions and tree inversions

A depth-first search version of Dhar's burning algorithm is used to give a bijection between the parking functions of a graph and labeled spanning trees, relating the degree of the parking function with the number of inversions of the spanning tree. Specializing to the complete graph answers a problem posed by R. Stanley.