Related papers: Parking Functions: Choose Your Own Adventure
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…
This paper presents an intelligent autonomous parking system with multi-functions. The integrated system consists of two sub-systems, namely the Fuzzy-Based Onboard System and control center. Unlike most current auto-parking experiments,…
In the near future, our streets will be populated by myriads of autonomous self-driving vehicles to serve our diverse mobility needs. This will raise the need to coordinate their movements in order to properly handle both access to shared…
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval…
Double parking that often negatively affects traffic operations and safety is not a new phenomenon on urban streets. This study proposes a novel data-driven integrated framework for estimating the actual frequency of double parking so that…
This is a survey paper on rainbow sets (another name for ``choice functions''). The main theme is the distinction between two types of choice functions: those having a large (in the sense of belonging to some specified filter, namely closed…
Unit-interval parking functions are subset of parking functions in which cars park at most one spot away from their preferred parking spot. In this paper, we characterize unit-interval parking functions by understanding how they decompose…
Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous slots, before proceedings forward as usual. In our…
This paper describes a smart parking sensing and information system that disseminates the parking availability information for public users in a cost-effective and efficient manner. The hardware framework of the system is built on advanced…
Given an undirected graph $G=(V,E)$, and a designated vertex $q\in V$, the notion of a $G$-parking function (with respect to $q$) was independently developed and studied by various authors, and has recently gained renewed attention. This…
In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the…
Current advances in the development of autonomous cars suggest that driverless cars may see wide-scale deployment in the near future. Research by both industry and academia is driven by potential benefits of this new technology, including…
We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are $n\in\mathbb{N}$ cars of lengths $\mathbf{y}=(y_1,y_2,\ldots,y_n)\in\mathbb{N}^n$ entering a one-way street…
This paper discusses the lexicographical concept of lexical functions and their potential exploitation in the development of a machine translation lexicon designed to handle collocations.
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted…
A classical parking function of length $n$ is a list of positive integers $(a_1, a_2, \ldots, a_n)$ whose nondecreasing rearrangement $b_1 \leq b_2 \leq \cdots \leq b_n$ satisfies $b_i \leq i$. The convex hull of all parking functions of…
Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair $(a,b)$, where $a$ is a…
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…
We propose a characterization of $k$-Naples parking functions in terms of subsequences with the structure of a complete $k$-Naples parking function. We define complete parking preferences by requiring that for all $j=2,\dots,n$, the number…
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…