Related papers: Pullback parking functions

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…

This paper provides an exploration of parking functions, a classical combinatorial object. We present two viewpoints on their structure and properties: through poset of noncrossing partitions and polytopes.

Parking plays a central role in transport policies and has wide-ranging consequences: While the average time spent searching for parking exceeds dozens of hours per driver every year in many Western cities, the associated cruising traffic…

For $\mathbf{b}=(b_1,\dots,b_n)\in \mathbb{Z}_{>0}^n$, a $\mathbf{b}$-parking function is defined to be a sequence $(\beta_1,\dots,\beta_n)$ of positive integers whose nondecreasing rearrangement $\beta'_1\leq \beta'_2\leq \cdots \leq…

We extend the notion of parking function polytopes and study their geometric and combinatorial structure, including normal fans, face posets, and $h$-polynomials, as well as their connections to other classes of polytopes. To capture their…

In a scenario of growing usage of park-and-ride facilities, understanding and predicting car park occupancy is becoming increasingly important. This study presents a model that effectively captures the occupancy patterns of park-and-ride…

Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Renyi's parking problem, alternatively called blocking…

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…

In this paper, we propose a new macro-micro approach to modeling parking. We first develop a microscopic parking simulation model considering both on- and off-street parking with limited capacity. In the microscopic model, a parking search…

We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its…

An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…

Inverse problems lend themselves naturally to a Bayesian formulation, in which the quantity of interest is a posterior distribution of state and/or parameters given some uncertain observations. For the common case in which the forward…

Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…

We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations…

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…

Let $W$ be an irreducible finite complex reflection group acting on a complex vector space $V$. For a positive integer $k$, we consider a class function $\varphi_k$ given by $\varphi_k(w) = k^{\dim V^w}$ for $w \in W$, where $V^w$ is the…

We enumerate a class of fully parked trees. In a probabilistic context, this means computing the partition function $F(x,y)$ of the parking process where an i.i.d. number of cars arrives at each vertex of a Galton-Watson tree with a…

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 Chebicheff polynomials having coefficients in the…

We deal with the problem of deriving the microscopic equations governing the individual car motion based on the assumptions about the strategy of driver behavior. We suppose the driver behavior to be a result of a certain compromise between…

We study lucky cars in subsets of parking functions, called Fubini rankings and unit Fubini rankings. A Fubini ranking is a sequence of nonnegative integers that encodes a valid ranking of competitors, where ties are allowed. A car (or…