Related papers: A Generalization of Parking Functions Allowing Bac…
An m-ballot path of size n is a path on the square grid consisting of north and east unit steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my. The set of these paths can be equipped with a lattice structure,…
In this paper, we generalize the Minkowski distance by defining a new distance function in n-dimensional space, and we show that this function determines also a metric family as the Minkowski distance. Then, we consider three special cases…
For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov. In two special cases, we show that the coefficients of this function when expanded in the complete homogeneous basis are…
The Totally Asymmetric Simple Exclusion Process (TASEP) is a paradigm of out-of-equilibrium Statistical Physics that serves as a simplistic model for one-way vehicular traffic. Since traffic is perturbed by cars cruising for parking in many…
We propose a generalized car parking problem where either a car of size $\sigma$ or of size $m\sigma$ ($m>1$) is sequentially parked on a line with probability $q$ and $(1-q)$, respectively. The free parameter $q$ interpolates between the…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
Current navigation systems conflate time-to-drive with the true time-to-arrive by ignoring parking search duration and the final walking leg. Such underestimation can significantly affect user experience, mode choice, congestion, and…
With the number of vehicles continuously increasing, parking monitoring and analysis are becoming a substantial feature of modern cities. In this study, we present a methodology to monitor car parking areas and to analyze their occupancy in…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
The purpose of this study is to introduce a new class of regular spaces called e*$\theta$-regular spaces which is a generalization of the class of $\beta\theta$-regular spaces. Also, we investigate some basic properties and several…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
Parking spaces are resources that can be pooled together and shared, especially when there are complementary day-time and night-time users. We answer two design questions. First, given a quality of service requirement, how many spaces…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
We settle a conjecture of B\'ona regarding the log-concavity of a certain statistic on parking functions by utilizing recent log-concavity results on matroids. This result allows us to also prove that connected, labeled graphs graded by…
We continue the study of parking assortments, a generalization of parking functions introduced by Chen, Harris, Mart\'{i}nez, Pab\'{o}n-Cancel, and Sargent. Given $n$ cars of lengths $\mathbf{y}=(y_1,y_2,\dots,y_n) \in \mathbb{N}^n$, we…
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence…
Stirling permutations are parking functions, and we investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results, we consider two extreme cases: extremely lucky Stirling…
We give a bijective proof of the fact that the number of k-prefixes of minimal factorisations of the n-cycle (1...n) as a product of n-1 transpositions is n^{k-1}\binom{n}{k+1}. Rather than a bijection, we construct a surjection with fibres…
When a human drives a car along a road for the first time, they later recognize where they are on the return journey typically without needing to look in their rear-view mirror or turn around to look back, despite significant viewpoint and…
In smart cities, it is common practice to define a maximum length of stay for a given parking space to increase the space's rotativity and discourage the usage of individual transportation solutions. However, automatically determining…