Related papers: A Generalization of Parking Functions Allowing Bac…
There are so many vehicles in the world and the number of vehicles is increasing rapidly. To alleviate the parking problems caused by that, the smart parking system has been developed. The parking planning is one of the most important parts…
We introduce a rather natural family of non-uniform distributions on $PF_n$, $n\in\mathbb{N}$, the set of parking functions of length $n$. One of the motivations for this comes from a similar situation in the context of integer partitions.…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
Transit functions were introduced as models of betweenness on undirected structures. Here we introduce directed transit function as the directed analogue on directed structures such as posets and directed graphs. We first show that…
The rapid development of automated driving systems in recent years has led to improvements in road safety and travel comfort. One typical function of these systems is Lane Keep Assist, which generally does not take human driving preferences…
All over the world, especially in the university environment, planning managers and traffic engineers are constantly faced with the problem of inadequate allocation of car parking spaces to demanded users. Users could either prefer reserved…
This paper proposes a totally asymmetric simple exclusion process on a traveling lane, which is equipped with a queueing system and functions of site assignments along the parking lane. In the proposed system, new particles arrive at the…
Let $d,k$ be positive integers. We call generalized spaces the cartesian product of the $d$-dimensional sphere, $\mathbb{S}^d$, with the $k$-dimensional Euclidean space, $\mathbb{R}^k$. We consider the class ${\mathcal P}(\mathbb{S}^d…
The Catalan numbers constitute one of the most important sequences in combinatorics. Catalan objects have been generalized in various directions, including the classical Fuss-Catalan objects and the rational Catalan generalization of…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
We test the umbral methods introduced by Rota and Taylor within the theory of representation of symmetric group. We define a simple bijection between the set of all parking functions of length $n$ and the set of all noncrossing partitions…
The cluster complex on one hand, parking functions on the other hand, are two combinatorial (po)sets that can be associated to a finite real reflection group. Cluster parking functions are obtained by taking an appropriate fiber product…
We define the $k$-dimensional generalized Euler function $\varphi_k(n)$ as the number of ordered $k$-tuples $(a_1,\ldots,a_k)\in {\Bbb N}^k$ such that $1\le a_1,\ldots,a_k\le n$ and both the product $a_1\cdots a_k$ and the sum $a_1+\cdots…
Let $\mathfrak{S}_n$ denote the symmetric group and let $W(\mathfrak{S}_n)$ denote the weak order of $\mathfrak{S}_n$. Through a surprising connection to a subset of parking functions, which we call unit Fubini rankings, we provide a…
The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter…
We recall the occupancy problem introduced by Konheim & Weiss in 1966 and we consider parking functions as hash maps. Each car $c_i$ prefers parking space $p_i$ (the hash map $c_i \mapsto p_i$ with $c_i$ is a key and $p_i$ an index into an…
The increasing availability and adoption of shared vehicles as an alternative to personally-owned cars presents ample opportunities for achieving more efficient transportation in cities. With private cars spending on the average over 95\%…
Many studies suggest that searching for parking is associated with significant direct and indirect costs. Therefore, it is appealing to reduce the time which car drivers spend on finding an available parking lot, especially in urban areas…
Consider the following simple parking process on $\Lambda_n := \{-n, \ldots, n\}^d,d\ge1$: at each step, a site $i$ is chosen at random in $\Lambda_n$ and if $i$ and all its nearest neighbor sites are empty, $i$ is occupied. Once occupied,…
Smart-parking solutions use sensors, cameras, and data analysis to improve parking efficiency and reduce traffic congestion. Computer vision-based methods have been used extensively in recent years to tackle the problem of parking lot…