Hodge theory in combinatorics
M Baker - Bulletin of the American Mathematical Society, 2018 - ams.org
If $ G $ is a finite graph, a proper coloring of $ G $ is a way to color the vertices of the graph
using $ n $ colors so that no two vertices connected by an edge have the same color.(The …
using $ n $ colors so that no two vertices connected by an edge have the same color.(The …
Maximum Likelihood Degree, Complete Quadrics, and -Action
We study the maximum likelihood (ML) degree of linear concentration models in algebraic
statistics. We relate it to an intersection problem on the variety of complete quadrics. This …
statistics. We relate it to an intersection problem on the variety of complete quadrics. This …
The geometry of matroids
F Ardila - Notices of the AMS, 2018 - ams.org
Matroid theory is a combinatorial theory of independence which has its origins in linear
algebra and graph theory and turns out to have deep connections with many other fields …
algebra and graph theory and turns out to have deep connections with many other fields …
The extremals of the Kahn-Saks inequality
R van Handel, A Yan, X Zeng - Advances in Mathematics, 2024 - Elsevier
A classical result of Kahn and Saks states that given any partially ordered set with two
distinguished elements, the number of linear extensions in which the ranks of the …
distinguished elements, the number of linear extensions in which the ranks of the …
Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral cones
P Aluffi - Advances in Mathematics, 2024 - Elsevier
We consider polynomials expressing the cohomology classes of subvarieties of products of
projective spaces, and limits of positive real multiples of such polynomials. We study the …
projective spaces, and limits of positive real multiples of such polynomials. We study the …
Log-Concave Sequences in Coding Theory
M Shi, X Wang, J An, JL Kim - arXiv preprint arXiv:2410.04412, 2024 - arxiv.org
We introduce the notion of logarithmically concave (or log-concave) sequences in Coding
Theory. A sequence $ a_0, a_1,\dots, a_n $ of real numbers is called log-concave if $ a_i …
Theory. A sequence $ a_0, a_1,\dots, a_n $ of real numbers is called log-concave if $ a_i …
Stanley–Reisner rings for symmetric simplicial complexes, -semimatroids and Abelian arrangements
A D'ali, E Delucchi - Journal of Combinatorial Algebra, 2021 - ems.press
We extend the notion of face rings of simplicial complexes and simplicial posets to the case
of finite-length (possibly infinite) simplicial posets with a group action. The action on the …
of finite-length (possibly infinite) simplicial posets with a group action. The action on the …
[PDF][PDF] An informal overview of triples and systems
LH Rowen - arXiv preprint arXiv:1709.03174, 2017 - arxiv.org
arXiv:1709.03174v5 [math.AC] 18 May 2018 Page 1 arXiv:1709.03174v5 [math.AC] 18 May
2018 AN INFORMAL OVERVIEW OF TRIPLES AND SYSTEMS LOUIS ROWEN Abstract. We …
2018 AN INFORMAL OVERVIEW OF TRIPLES AND SYSTEMS LOUIS ROWEN Abstract. We …
Logarithmic concavity of bimatroids
F Röhrle, M Ulirsch - arXiv preprint arXiv:2402.15317, 2024 - arxiv.org
A bimatroid is a matroid-like generalization of the collection of regular minors of a matrix. In
this article, we use the theory of Lorentzian polynomials to study the logarithmic concavity of …
this article, we use the theory of Lorentzian polynomials to study the logarithmic concavity of …
The augmented external activity complex of a matroid
A Berget, D Morales - arXiv preprint arXiv:2401.17470, 2024 - arxiv.org
For a matroid, we define a new simplicial complex whose facets are indexed by its
independent sets. This complex contains the external activity complex as a subcomplex. We …
independent sets. This complex contains the external activity complex as a subcomplex. We …