Related papers: Parking functions and Haglund--Loehr data

Apr\`es avoir pos\'e les d\'efinitions n\'ecessaires \`a la compr\'ehension du sujet, nous discuterons de statistique d'inversion diagonale dans les $r$-Schr\"oder, de chemins de stationnement dans les $r$-Schr\"oder \`a pente enti\`ere et…

This article proposes two different approaches to automatically create a map for valid on-street car parking spaces. For this, we use car sharing park-out events data. The first one uses spatial aggregation and the second a machine learning…

We define two classes of functions, called regular (respectively, first-order) list functions, which manipulate objects such as lists, lists of lists, pairs of lists, lists of pairs of lists, etc. The definition is in the style of regular…

Tiered trees were introduced as a combinatorial object for counting absolutely indecomposable representation of certain quivers and torus orbit of certain homogeneous variety. In this paper, we define a bijection between the set of…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…

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.…

We define two actions of the infinite symmetric group on the set of words on positive integers, called the free and parking quasi-symmetrizing actions, whose invariants are respectively the elements of the Hopf algebras $\textbf{FQSym}^*$…

For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…

We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric…

Smart cities around the world have begun monitoring parking areas in order to estimate available parking spots and help drivers looking for parking. The current results are promising, indeed. However, existing approaches are limited by the…

Back in the nineties Pak and Stanley introduced a labeling of the regions of a k-Shi arrangement by k-parking functions and proved its bijectivity. Duval, Klivans, and Martin considered a modification of this construction associated with a…

The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…

Parking functions are well researched and interesting results are found in the listed references and more. Some introductory results stemming from application to degree sequences of simple connected graphs are provided in this paper.…

We give new equations which characterize the generating functions of planar quadrangulations and planar triangulations, with zero, one or two boundaries. The proof is inspired by the Lackner--Panholzer last car decomposition of parking…

We prove that the combinatorial side of the "Rational Shuffle Conjecture" provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT…

Let $N(n,r,k)$ denote the number of binary words of length $n$ that begin with $0$ and contain exactly $k$ runs (i.e., maximal subwords of identical consecutive symbols) of length $r$. We show that the generating function for the sequence…

The action of the symmetric group $S_n$ on the set $Park_n$ of parking functions of size $n$ has received a great deal of attention in algebraic combinatorics. We prove that the action of $S_n$ on $Park_n$ extends to an action of $S_{n+1}$.…

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…