Parking Policy as a Tool of Sustainable Mobility-Parking Standards in Poland vs. European Experiences

Contemporary cities generally lack the balance between the development of the spatial structure and the communication possibilities of the inhabitants. The high motorisation rate in Poland, as well as in other European countries, and the preferred choice of individual means of transportation have both contributed to a significant increase in congestion over the last 10 years. The aim of this research was to try to establish to what extent a consciously conducted parking policy can help control the mobility of inhabitants of selected Polish cities. The starting point for the analysis was the availability of parking spaces in residential areas, introduced as an imposed indicator in the operative planning documents. As part of the research, the authors of this paper analyzed the legal provisions of the operative Local Spatial Development Plans (MPZP) concerning the parking function for housing estates five of the biggest cities in Poland. The results were confronted with data on selected European cities. Nearly 550 planning documents from the years 2000–2019 and parking standards operating in individual countries were cataloged and analyzed. The research results show that for 20 years Polish cities have mainly been using the possibility of determining the minimum rate of parking spaces. Regulations attempting to limit the number of cars are incidental. However, this is a necessary direction of legislative changes.

Skeleton Ideals of Certain Graphs, Standard Monomials and Spherical Parking Functions

Let $G$ be a graph on the vertex set $V = \{ 0, 1,\ldots,n\}$ with root $0$. Postnikov and Shapiro were the first to consider a monomial ideal $\mathcal{M}_G$, called the $G$-parking function ideal, in the polynomial ring $ R = {\mathbb{K}}[x_1,\ldots,x_n]$ over a field $\mathbb{K}$ and explained its connection to the chip-firing game on graphs. The standard monomials of the Artinian quotient $\frac{R}{\mathcal{M}_G}$ correspond bijectively to $G$-parking functions. Dochtermann introduced and studied skeleton ideals of the graph $G$, which are subideals of the $G$-parking function ideal with an additional parameter $k ~(0\le k \le n-1)$. A $k$-skeleton ideal $\mathcal{M}_G^{(k)}$ of the graph $G$ is generated by monomials corresponding to non-empty subsets of the set of non-root vertices $[n]$ of size at most $k+1$. Dochtermann obtained many interesting homological and combinatorial properties of these skeleton ideals. In this paper, we study the $k$-skeleton ideals of graphs and for certain classes of graphs provide explicit formulas and combinatorial interpretation of standard monomials and the Betti numbers.

A Generalization of Parking Functions Allowing Backward Movement

Classical parking functions are defined as the parking preferences for $n$ cars driving (from west to east) down a one-way street containing parking spaces labeled from $1$ to $n$ (from west to east). Cars drive down the street toward their preferred spot and park there if the spot is available. Otherwise, the car continues driving down the street and takes the first available parking space, if such a space exists. If all cars can park using this parking rule, we call the $n$-tuple containing the cars' parking preferences a parking function. In this paper, we introduce a generalization of the parking rule allowing cars whose preferred space is taken to first proceed up to $k$ spaces west of their preferred spot to park before proceeding east if all of those $k$ spaces are occupied. We call parking preferences which allow all cars to park under this new parking rule $k$-Naples parking functions of length $n$. This generalization gives a natural interpolation between classical parking functions, the case when $k=0$, and all $n$-tuples of positive integers $1$ to $n$, the case when $k\geq n-1$. Our main result provides a recursive formula for counting $k$-Naples parking functions of length $n$. We also give a characterization for the $k=1$ case by introducing a new function that maps $1$-Naples parking functions to classical parking functions, i.e. $0$-Naples parking functions. Lastly, we present a bijection between $k$-Naples parking functions of length $n$ whose entries are in weakly decreasing order and a family of signature Dyck paths.

Intelligent Traffic System Design Research of Urban Complex Underground Garage

Reasonable traffic system design and management has vital significance to ensure the safe and smooth traffic operation of urban complex and urban traffic system. Based on the characteristics of urban complex, this paper analyzed intelligent traffic system design of underground garage of urban complex. The paper proposed a reasonable traffic system design method to ensure the smoothness and safety of urban complex traffic. Meanwhile the full-video intelligent parking garage management system with advantages of safe and advanced technology was adopted to realize user-friendly, intelligent and automation traffic management. Through intelligent traffic system design research of urban complex underground garage proposed in this paper, the operation efficiency of the underground garage was improved and the parking function and evacuation capacity of underground garage was brought into full play.