2 citations · 5 across the 20 of their papers we have counts for
21 papers
Ehrhart -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 -polynomial of a lattice polytope is a non-n…
Lattice slices, Ehrhart polynomials, and magic positivity of generalized parking-function polytopes
Charlie Hill, Ambrose Luo, Vu Trinh +1
For , a -parking function is a sequence of positive integers whose nondecreasing rearrangement $β_1'\l…
Generating Trees and Fibonacci Polyominoes
Juan F. Pulido, José L. Ramírez, Andrés R. Vindas-Meléndez
We study a new class of polyominoes, called -Fibonacci polyominoes, defined using -Fibonacci words. We enumerate these polyominoes by applying generating functions to capture…
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…
Polyhedral geometry of refined -Catalan numbers
Matthias Beck, Mitsuki Hanada, Max Hlavacek +3
We study a refinement of the -Catalan numbers introduced by Xin and Zhang (2022, 2023) using tools from polyhedral geometry. These refined -Catalan numbers depend on a ve…
Matching polytopes, Gorensteinness, and the integer decomposition property
Benjamin Eisley, Koji Matsushita, Andrés R. Vindas-Meléndez
The matching polytope of a graph is the convex hull of the indicator vectors of the matchings on . We characterize the graphs whose associated matching polytopes are Gorenst…
Combinatorics of generalized parking-function polytopes
Margaret M. Bayer, Steffen Borgwardt, Teressa Chambers +8
For , a -parking function is defined to be a sequence of positive integers whose nondecreasing rearra…
-Chromatic polynomials
Esme Bajo, Matthias Beck, Andrés R. Vindas-Meléndez
We study a -version of the chromatic polynomial of a given graph , namely, \[ χ_G^λ(q,n) \ := \sum_{\substack{\text{proper colorings}\\ c\,:\,V\to[n]}} q^{ \sum_{ v \in…
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…
Local -polynomials for one-row Hermite normal form simplices
Esme Bajo, Benjamin Braun, Giulia Codenotti +2
The local -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…
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 permutations, i.e., permutat…
Quantifying and Documenting Inequity in PhD-granting Mathematical Sciences Departments in the United States
Ron Buckmire, Carrie Diaz Eaton, Joseph E. Hibdon +6
We provide an example of the application of quantitative techniques, tools, and topics from mathematics and data science to analyze the mathematics community itself in order to qua…
The Mathematics of Mathematics: Using Mathematics and Data Science to Analyze the Mathematical Sciences Community and Enhance Social Justice
Ron Buckmire, Joseph E. Hibdon, Drew Lewis +4
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have…
On definitions of "mathematician"
Ron Buckmire, Carrie Diaz Eaton, Joseph E. Hibdon +6
The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is…
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 is t…
Generalized parking function polytopes
Mitsuki Hanada, John Lentfer, Andrés R. Vindas-Meléndez
A classical parking function of length is a list of positive integers whose nondecreasing rearrangement satisfies…
On the critical group of hinge graphs
Aren Martinian, Andrés R. Vindas-Meléndez
Let be a finite, connected, simple graph. The critical group , also known as the sandpile group, is the torsion subgroup of the cokernel of the graph Laplacian $\operator…
Enumerating -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 -Naples parking functions, where backward movement is allowed. One consequence of backward movement is that the nu…
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…
Counting -Naples parking functions through permutations and the -Naples area statistic
Laura Colmenarejo, Pamela E. Harris, Zakiya Jones +4
We recall that the -Naples parking functions of length (a generalization of parking functions) are defined by requiring that a car which finds its preferred spot occupied mu…
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…