On lattice path matroid polytopes: integer points and Ehrhart polynomial
K Knauer, L Martínez-Sandoval… - Discrete & Computational …, 2018 - Springer
In this paper we investigate the number of integer points lying in dilations of lattice path
matroid polytopes. We give a characterization of such points as polygonal paths in the …
matroid polytopes. We give a characterization of such points as polygonal paths in the …
Ehrhart theory of paving and panhandle matroids
D Hanely, JL Martin, D McGinnis, D Miyata… - Advances in …, 2023 - degruyter.com
We show that the base polytope PM of any paving matroid M can be systematically obtained
from a hypersimplex by slicing off certain subpolytopes, namely base polytopes of lattice …
from a hypersimplex by slicing off certain subpolytopes, namely base polytopes of lattice …
Lattice path matroids and quotients
C Benedetti, K Knauer - arXiv preprint arXiv:2202.11634, 2022 - arxiv.org
We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams.
This characterization allows us to show that ordering LPMs by quotients yields a graded …
This characterization allows us to show that ordering LPMs by quotients yields a graded …
Lattice Path Matroids and Quotients
C Benedetti-Velásquez, K Knauer - Combinatorica, 2024 - Springer
We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams.
This characterization allows us to show that ordering LPMs by quotients yields a graded …
This characterization allows us to show that ordering LPMs by quotients yields a graded …
[HTML][HTML] A Tutte polynomial inequality for lattice path matroids
K Knauer, L Martínez-Sandoval, JLR Alfonsín - Advances in Applied …, 2018 - Elsevier
Let M be a matroid without loops or coloops and let T (M; x, y) be its Tutte polynomial. In
1999 Merino and Welsh conjectured that max(T (M; 2, 0), T (M; 0, 2))≥ T (M; 1, 1) holds for …
1999 Merino and Welsh conjectured that max(T (M; 2, 0), T (M; 0, 2))≥ T (M; 1, 1) holds for …
[HTML][HTML] Facial structures of lattice path matroid polytopes
S An, JY Jung, S Kim - Discrete Mathematics, 2020 - Elsevier
A lattice path matroid is a transversal matroid corresponding to a pair of lattice paths on the
plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of …
plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of …
Lattice path matroidal subdivisions, Positive Tropical Grassmannian and Amplituhedron
AK Tewari, AU Ashraf - arXiv preprint arXiv:2307.04180, 2023 - arxiv.org
We introduce the notion of lattice path matroidal subdivisions, or LPM subdivisions for short,
and show that these subdivisions are regular and hence the weight vectors for them lie in …
and show that these subdivisions are regular and hence the weight vectors for them lie in …
Derived Categories of Permutahedral and Stellahedral Varieties
M Sanchez - arXiv preprint arXiv:2311.04203, 2023 - arxiv.org
We utilize the coherent-constructible correspondence to construct full strongly exceptional
collections of nef line bundles in the derived category of a toric variety through the …
collections of nef line bundles in the derived category of a toric variety through the …
Eulerian-catalan numbers
H Bidkhori, S Sullivant - arXiv preprint arXiv:1101.1108, 2011 - arxiv.org
arXiv:1101.1108v1 [math.CO] 5 Jan 2011 Page 1 arXiv:1101.1108v1 [math.CO] 5 Jan 2011
Eulerian-Catalan Numbers Hoda Bidkhori Department of Mathematics North Carolina State …
Eulerian-Catalan Numbers Hoda Bidkhori Department of Mathematics North Carolina State …
Lattice Path Delta Matroids
DM Chen, M Sanchez, J Veliz, Z Ying - arXiv preprint arXiv:2311.15441, 2023 - arxiv.org
We initiate the study of a type $ C_n $ generalization of the lattice path matroids defined by
Bonin, de Mier, and Noy. These are delta matroids whose feasible sets are in bijection with …
Bonin, de Mier, and Noy. These are delta matroids whose feasible sets are in bijection with …