Related papers: Parking functions for trees and mappings
Traffic prediction is a spatiotemporal predictive task that plays an essential role in intelligent transportation systems. Today, graph convolutional neural networks (GCNNs) have become the prevailing models in the traffic prediction…
Treewidth is a well-known graph invariant with multiple interesting applications in combinatorics. On the practical side, many NP-complete problems are polynomial-time (sometimes even linear-time) solvable on graphs of bounded treewidth. On…
There are different functional regions in cities such as tourist attractions, shopping centers, workplaces and residential places. The human mobility patterns for different functional regions are different, e.g., people usually go to work…
Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused…
In this paper, let $\mathcal{P}_{n;\leq s;k}^l$ denote a set of $k$-flaw preference sets $(a_1,...,a_n)$ with $n$ parking spaces satisfying that $1\leq a_i\leq s$ for any $i$ and $a_1=l$ and $p_{n;\leq s;k}^l=|\mathcal{P}_{n;\leq s;k}^l|$.…
The Theory of Functional Connections (TFC) is most often used for constraints over the field of real numbers. However, previous works have shown that it actually extends to arbitrary fields. The evidence for these claims is restricting…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with…
On a countable tree $T$, allowing vertices with infinite degree, we consider an arbitrary stochastic irreducible nearest neighbour transition operator $P$. We provide a boundary integral representation for general eigenfunctions of $P$ with…
We study higher-dimensional analogues of graph-theoretic trees within the class of pure n-simplicial complexes. Focusing on the case m = n-1 in Dewdney's (m, n)-tree framework, we introduce refined notions of path and circuit sequences that…
Consider the following simple parking process on $\Lambda_n := \{-n, \ldots, n\}^d,d\ge1$: at each step, a site $i$ is chosen at random in $\Lambda_n$ and if $i$ and all its nearest neighbor sites are empty, $i$ is occupied. Once occupied,…
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…
Tracking the movement of tracer particles has long been a strategy for uncovering complex structures. Here, we study discrete-time random walks on finite Cayley trees to infer key parameters such as tree depth and geometric bias toward the…
In 1980, G. Kreweras gave a recursive bijection between forests and parking functions. In this paper we construct a nonrecursive bijection from forests onto parking functions, which answers a question raised by R. Stanley. As a by-product,…
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…
We give a very short proof of the fact that the number of $(a,b)$-parking functions of length $n$ equals $a(a+bn)^{n-1}$. This was first proved in 2003 by Kung and Yan, via a very long and torturous route, as a corollary of a more general…
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.…
We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the functional distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work,…
We define the disposition polynomial $R_{m}(x_1, x_2, ..., x_n)$ as $\prod_{k=0}^{m-1}(x_1+x_2+...+x_n+k)$. When $m=n-1$, this polynomial becomes the generating function of plane trees with respect to certain statistics as given by Guo and…