Related papers: On the connected blocks polytope
The Birkhoff polytope, defined to be the convex hull of $n\times n$ permutation matrices, is a well studied polytope in the context of the Ehrhart theory. This polytope is known to have many desirable properties, such as the Gorenstein…
We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of all matchings, extended by a binary entry indicating whether the matching contains two specific edges. These polytopes are associated to the quadratic…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…
In this paper, we give a criterion of the nearly Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ with connected components…
We classify connected graphs $G$ whose binomial edge ideal is Gorenstein. The proof uses methods in prime characteristic.
Starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. The first goal of this paper is to show that symmetric edge polytopes are intrinsically matroidal objects: more precisely, we…
In this paper we give several criteria for the edge polytope of a fundamental FHM-graph to possess a regular unimodular triangulation in terms of some simple data of the the graph. We further apply our criteria to several examples of graphs…
We identify a family of $O(|E(G)|^2)$ nontrivial facets of the connected matching polytope of a graph $G$, that is, the convex hull of incidence vectors of matchings in $G$ whose covered vertices induce a connected subgraph. Accompanying…
Let $I_G$ be the binomial edge ideal on the generic 2 x n - Hankel matrix associated with a closed graph $G$ on the vertex set [n]. We characterize the graphs $G$ for which $I_G$ has maximal regularity and is Gorenstein.
The perfectly matchable subgraph polytope of a graph is a (0,1)-polytope associated with the vertex sets of matchings in the graph. In this paper, we study algebraic properties (compressedness, Gorensteinness) of the toric rings of…
Graph polytopes arising from vertex-weighted graphs were first introduced by B\'ona, Ju, and Yoshida. We prove a conjecture stating that for any simple connected graph, the numerator polynomial of the Ehrhart series of its graph polytope is…
A level graph is the data of a pair $(G,\pi)$ consisting of a finite graph $G$ and an ordered partition $\pi$ on the set of vertices of $G$. To each level graph on $n$ vertices we associate a polytope in $\mathbb R^n$ called its residue…
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least $2k$ vertices is $k$-linked if, for every…
We introduce the cohomological blow up of a graded Artinian Gorenstein (AG) algebra along a surjective map, which we term BUG (Blow Up Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a…
We study a symmetry problem for the $h$-polynomials of edge rings of bipartite graphs. Let $G$ be a bipartite graph and write $h(\mathbb{k}[G];t)=h_0+h_1t+\cdots+h_st^s$. We prove that if $\Bbbk[G]$ is pseudo-Gorenstein and $h_1=h_{s-1}$,…
In Ehrhart theory, the $h^*$-vector of a rational polytope often provide insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic…
(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…
Given any polytope $P$ and any generic linear functional ${\bf c} $, one obtains a directed graph $G(P,{\bf c})$ from the 1-skeleton of $P$ by orienting each edge $e(u,v)$ from $u$ to $v$ for ${\bf c} (u) < {\bf c} ( v)$. For $P$ a simple…
In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…