Andrés R. Vindas-Meléndez

activity

20182026

most citedGeneralized parking function polytopes

2 citations · 5 across the 20 of their papers we have counts for

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18 papers · 1 filter

math.CO2026

Ehrhart $h^{*}$ -distributions

Benjamin Braun, Max Hlavacek, Cesar J. Meza +2

Every polynomial with real non-negative coefficients yields a finite probability distribution after normalization. The Ehrhart $h^{*}$ -polynomial of a lattice polytope $P$ is a non-n…

math.CO2026

Lattice slices, Ehrhart polynomials, and magic positivity of generalized parking-function polytopes

Charlie Hill, Ambrose Luo, Vu Trinh +1

For $b = (b_{1}, \dots, b_{n}) \in Z_{> 0}^{n}$ , a $b$ -parking function is a sequence $(β_{1}, \dots, β_{n})$ of positive integers whose nondecreasing rearrangement $β_1'\l…

math.CO2024

Generating Trees and Fibonacci Polyominoes

Juan F. Pulido, José L. Ramírez, Andrés R. Vindas-Meléndez

We study a new class of polyominoes, called $p$ -Fibonacci polyominoes, defined using $p$ -Fibonacci words. We enumerate these polyominoes by applying generating functions to capture…

math.CO2024

Generalized snake posets, order polytopes, and lattice-point enumeration

Eon Lee, Andrés R. Vindas-Meléndez, Zhi Wang

Building from the work of von Bell et al.~(2022), we study the Ehrhart theory of order polytopes arising from a special class of distributive lattices, known as generalized snake p…

math.CO2024

Polyhedral geometry of refined $q, t$ -Catalan numbers

Matthias Beck, Mitsuki Hanada, Max Hlavacek +3

We study a refinement of the $q, t$ -Catalan numbers introduced by Xin and Zhang (2022, 2023) using tools from polyhedral geometry. These refined $q, t$ -Catalan numbers depend on a ve…

math.CO2024

Matching polytopes, Gorensteinness, and the integer decomposition property

Benjamin Eisley, Koji Matsushita, Andrés R. Vindas-Meléndez

The matching polytope of a graph $G$ is the convex hull of the indicator vectors of the matchings on $G$ . We characterize the graphs whose associated matching polytopes are Gorenst…

math.CO2024

Combinatorics of generalized parking-function polytopes

Margaret M. Bayer, Steffen Borgwardt, Teressa Chambers +8

For $b = (b_{1}, \dots, b_{n}) \in Z_{> 0}^{n}$ , a $b$ -parking function is defined to be a sequence $(β_{1}, \dots, β_{n})$ of positive integers whose nondecreasing rearra…

math.CO2024

$q$ -Chromatic polynomials

Esme Bajo, Matthias Beck, Andrés R. Vindas-Meléndez

We study a $q$ -version of the chromatic polynomial of a given graph $G = (V, E)$ , namely, \[ χ_G^λ(q,n) \ := \sum_{\substack{\text{proper colorings}\\ c\,:\,V\to[n]}} q^{ \sum_{ v \in…

math.CO2023

Ehrhart Bounds for Panhandle and Paving Matroids Through Enumeration of Chain Forests

Danai Deligeorgaki, Daniel McGinnis, Andrés R. Vindas-Meléndez

Panhandle matroids are a specific family of lattice-path matroids corresponding to panhandle-shaped Ferrers diagrams. Their matroid polytopes are the subpolytopes carved from a hyp…

math.CO2023★ 1 cited

Local $h^{*}$ -polynomials for one-row Hermite normal form simplices

Esme Bajo, Benjamin Braun, Giulia Codenotti +2

The local $h^{*}$ -polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus is on lattice simplices presented in Hermite normal form with a sing…

math.CO2023

Stack-sorting simplices: geometry and lattice-point enumeration

Eon Lee, Carson Mitchell, Andrés R. Vindas-Meléndez

We initiate the study of subpolytopes of the permutahedron that arise as the convex hulls of stack-sorting on permutations. We primarily focus on $L n 1$ permutations, i.e., permutat…

math.CO2022★ 2 cited

A combinatorial proof of a symmetry for a refinement of the Narayana numbers

Miklós Bóna, Stoyan Dimitrov, Gilbert Labelle +4

We establish a tantalizing symmetry of certain numbers refining the Narayana numbers. In terms of Dyck paths, this symmetry is interpreted in the following way: if $w_{n, k, m}$ is t…

math.CO2022★ 2 cited

Generalized parking function polytopes

Mitsuki Hanada, John Lentfer, Andrés R. Vindas-Meléndez

A classical parking function of length $n$ is a list of positive integers $(a_{1}, a_{2}, \dots, a_{n})$ whose nondecreasing rearrangement $b_{1} \leq b_{2} \leq \dots \leq b_{n}$ satisfies…

math.CO2022

On the critical group of hinge graphs

Aren Martinian, Andrés R. Vindas-Meléndez

Let $G$ be a finite, connected, simple graph. The critical group $K (G)$ , also known as the sandpile group, is the torsion subgroup of the cokernel of the graph Laplacian $\operator…

math.CO2021

Enumerating $k$ -Naples Parking Functions Through Catalan Objects

João Pedro Carvalho, Pamela E. Harris, Gordon Rojas Kirby +2

This paper studies a generalization of parking functions named $k$ -Naples parking functions, where backward movement is allowed. One consequence of backward movement is that the nu…

math.CO2021

Triangulations, order polytopes, and generalized snake posets

Matias von Bell, Benjamin Braun, Derek Hanely +4

This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same r…

math.CO2020

Counting $k$ -Naples parking functions through permutations and the $k$ -Naples area statistic

Laura Colmenarejo, Pamela E. Harris, Zakiya Jones +4

We recall that the $k$ -Naples parking functions of length $n$ (a generalization of parking functions) are defined by requiring that a car which finds its preferred spot occupied mu…

math.CO2018

A Brief Survey on Lattice Zonotopes

Benjamin Braun, Andrés R. Vindas-Meléndez

Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results r…

Ehrhart h∗-distributions

Lattice slices, Ehrhart polynomials, and magic positivity of generalized parking-function polytopes

Generating Trees and Fibonacci Polyominoes

Generalized snake posets, order polytopes, and lattice-point enumeration

Polyhedral geometry of refined q,t-Catalan numbers

Matching polytopes, Gorensteinness, and the integer decomposition property

Combinatorics of generalized parking-function polytopes

q-Chromatic polynomials

Ehrhart Bounds for Panhandle and Paving Matroids Through Enumeration of Chain Forests

Local h∗-polynomials for one-row Hermite normal form simplices

Stack-sorting simplices: geometry and lattice-point enumeration

A combinatorial proof of a symmetry for a refinement of the Narayana numbers

Generalized parking function polytopes

On the critical group of hinge graphs

Enumerating k-Naples Parking Functions Through Catalan Objects

Triangulations, order polytopes, and generalized snake posets

Counting k-Naples parking functions through permutations and the k-Naples area statistic

A Brief Survey on Lattice Zonotopes

Ehrhart $h^{*}$ -distributions

Polyhedral geometry of refined $q, t$ -Catalan numbers

$q$ -Chromatic polynomials

Local $h^{*}$ -polynomials for one-row Hermite normal form simplices

Enumerating $k$ -Naples Parking Functions Through Catalan Objects

Counting $k$ -Naples parking functions through permutations and the $k$ -Naples area statistic