Valuative invariants for large classes of matroids
L Ferroni, B Schröter - Journal of the London Mathematical …, 2024 - Wiley Online Library
We study an operation in matroid theory that allows one to transition a given matroid into
another with more bases via relaxing a stressed subset. This framework provides a new …
another with more bases via relaxing a stressed subset. This framework provides a new …
[HTML][HTML] Matroids are not Ehrhart positive
L Ferroni - Advances in Mathematics, 2022 - Elsevier
In this article we disprove the conjectures asserting the positivity of the coefficients of the
Ehrhart polynomial of matroid polytopes by De Loera, Haws and Köppe (2007) and of …
Ehrhart polynomial of matroid polytopes by De Loera, Haws and Köppe (2007) and of …
[HTML][HTML] Ehrhart polynomials of rank two matroids
Over a decade ago De Loera, Haws and Köppe conjectured that Ehrhart polynomials of
matroid polytopes have only positive coefficients and that the coefficients of the …
matroid polytopes have only positive coefficients and that the coefficients of the …
A regular unimodular triangulation of the matroid base polytope
S Backman, G Liu - arXiv preprint arXiv:2309.10229, 2023 - arxiv.org
arXiv:2309.10229v1 [math.CO] 19 Sep 2023 Page 1 arXiv:2309.10229v1 [math.CO] 19 Sep
2023 A REGULAR UNIMODULAR TRIANGULATION OF THE MATROID BASE POLYTOPE …
2023 A REGULAR UNIMODULAR TRIANGULATION OF THE MATROID BASE POLYTOPE …
Decomposition Polyhedra of Piecewise Linear Functions
MC Brandenburg, M Grillo, C Hertrich - arXiv preprint arXiv:2410.04907, 2024 - arxiv.org
In this paper we contribute to the frequently studied question of how to decompose a
continuous piecewise linear (CPWL) function into a difference of two convex CPWL …
continuous piecewise linear (CPWL) function into a difference of two convex CPWL …
Lattice points in slices of prisms
L Ferroni, D McGinnis - Canadian Journal of Mathematics, 2022 - cambridge.org
We conduct a systematic study of the Ehrhart theory of certain slices of rectangular prisms.
Our polytopes are generalizations of the hypersimplex and are contained in the larger class …
Our polytopes are generalizations of the hypersimplex and are contained in the larger class …
On the Todd class of the permutohedral variety
F Castillo, F Liu - Algebraic Combinatorics, 2021 - numdam.org
In the special case of braid fans, we give a combinatorial formula for the Berline–Vergne's
construction for an Euler–Maclaurin type formula that computes the number of lattice points …
construction for an Euler–Maclaurin type formula that computes the number of lattice points …
Combinatorics of generalized parking-function polytopes
MM Bayer, S Borgwardt, T Chambers… - arXiv preprint arXiv …, 2024 - arxiv.org
For $\mathbf {b}=(b_1,\dots, b_n)\in\mathbb {Z} _ {> 0}^ n $, a $\mathbf {b} $-parking function
is defined to be a sequence $(\beta_1,\dots,\beta_n) $ of positive integers whose …
is defined to be a sequence $(\beta_1,\dots,\beta_n) $ of positive integers whose …
On combinatorial descriptions of faces of the cone of supermodular functions
M Studený - arXiv preprint arXiv:2410.19454, 2024 - arxiv.org
Five different ways of combinatorial description of non-empty faces of the cone of
supermodular functions on the power set of a finite basic set $ N $ are introduced. Their …
supermodular functions on the power set of a finite basic set $ N $ are introduced. Their …
Ehrhart Positivity of Panhandle Matroids and the Ehrhart-Coefficient Upper-Bound Conjecture for Paving Matroids
D Deligeorgaki, D McGinnis… - arXiv preprint arXiv …, 2023 - arxiv.org
Panhandle matroids are a specific lattice-path matroid corresponding to panhandle-shaped
Ferrers diagrams. Their matroid polytopes are the subpolytopes carved from a hypersimplex …
Ferrers diagrams. Their matroid polytopes are the subpolytopes carved from a hypersimplex …