Related papers: Enumerating Vector Parking Functions and their Out…
We define a generalized vector partition function and derive an identity for generating series of such functions associated with solutions of basic recurrence relation of combinatorial analysis. As a consequence, we obtain the generating…
Consider a uniform random rooted tree on vertices labelled by $[n] = \{1,2,\ldots,n\}$, with edges directed towards the root. We imagine that each node of the tree has space for a single car to park. A number $m \le n$ of cars arrive one by…
Finding an available on-street parking spot is a relevant problem of day-to-day life. In recent years, cities such as Melbourne and San Francisco deployed sensors that provide real-time information about the occupation of parking spots.…
Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence with planar Eulerian (i.e., bicolored) maps.…
Growing advancements in reinforcement learning has led to advancements in control theory. Reinforcement learning has effectively solved the inverted pendulum problem and more recently the double inverted pendulum problem. In reinforcement…
Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$ to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of $G$-parking functions. In particular, we…
The objective behind this project is to maximize the efficiency of land space, to decrease the driver stress and frustration, along with a considerable reduction in air pollution. Our contribution is in the form of an automatic parking…
We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…
This paper aims to develop a robust and flexible algorithm for vacant parking space detections using the image processing capabilities of OpenCV. It removes the need for independent sensors to detect a car and instead, uses real-time images…
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…
The parking issue is central in transport policies and drivers' concerns, but the determinants of the parking search time remain relatively poorly understood. The question is often handled in a fairly ad hoc way, or by resorting to crude…
Our main result is an explicit operator-theoretic formula for the number of colored planar maps with a fixed set of stars each of which has a fixed set of half-edges with fixed coloration. The formula bounds the number of such colored…
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…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…
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…
This paper introduces a comprehensive approach to optimize parking efficiency for connected and Automated vehicle (CAVs) fleets. We present a multi-vehicle parking simulator, equipped with hierarchical path planning and collision avoidance…
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…
We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By…
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…
To provide real-time parking information, existing studies focus on predicting parking availability, which seems an indirect approach to saving drivers' cruising time. In this paper, we first time propose an on-street parking recommendation…