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Ehrhart Quasi-Polynomials of Almost Integral Polytopes
A lattice polytope translated by a rational vector is called an almost integral polytope. In this paper, we study Ehrhart quasi-polynomials of almost...
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On the Ehrhart Polynomial of Schubert Matroids
In this paper, we give a formula for the number of lattice points in the dilations of Schubert matroid polytopes. As applications, we obtain the...
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The Characterisation Problem of Ehrhart Polynomials of Lattice Polytopes
One of the most important invariants of a lattice polytope is the Ehrhart polynomial. The problem of which polynomials can be Ehrhart polynomials of...
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Restricted Birkhoff Polytopes and Ehrhart Period Collapse
We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the “longest increasing subsequence”...
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Chainlink Polytopes and Ehrhart Equivalence
We introduce a class of polytopes that we call chainlink polytopes and show that they allow us to construct infinite families of pairs of...
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Techniques in Equivariant Ehrhart Theory
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group...
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Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials
Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial...
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On the Ehrhart Polynomial of Minimal Matroids
We provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal...
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Ehrhart Theory and the Seiberg–Witten Invariant
We study the Seiberg-Witten invariant via the multivariable (combinatorial) series associated with the resolution graphs and certain quasipolynomials...
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Cubic Graphs, Their Ehrhart Quasi-Polynomials, and a Scissors Congruence Phenomenon
The scissors congruence conjecture for the unimodular group is an analogue of Hilbert’s third problem, for the equidecomposability of polytopes. Liu...
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Binomial Inequalities for Chromatic, Flow, and Tension Polynomials
A famous and wide-open problem, going back to at least the early 1970s, concerns the classification of chromatic polynomials of graphs. Toward this...
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Lower bounds for contingency tables via Lorentzian polynomials
We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok [Bar09, Bar16] and...
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Postnikov–Stanley Linial arrangement conjecture
A characteristic polynomial is an important invariant in the field of hyperplane arrangement. For the Linial arrangement of any irreducible root...
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An algebra over the operad of posets and structural binomial identities
We study generating functions of strict and non-strict order polynomials of series–parallel posets, called order series. These order series are...
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Discrete Equidecomposability and Ehrhart Theory of Polygons
Motivated by questions from Ehrhart theory, we present new results on discrete equidecomposability. Two rational polygons P and Q are said to be discre...
