• Corpus ID: 246275684

Ehrhart theory of symmetric edge polytopes via ribbon structures

  title={Ehrhart theory of symmetric edge polytopes via ribbon structures},
  author={Tam'as K'alm'an and Lilla T'othm'er'esz},
Using a ribbon structure of the graph, we construct a dissection of the symmetric edge polytope of a graph into unimodular simplices. Our dissection is shellable, and one can interpret the elements of the resulting hvector via graph theory. This gives an elementary method for computing the h∗-vector of the symmetric edge polytope. 

$h^*$-vectors of graph polytopes using activities of dissecting spanning trees

. Both for symmetric edge polytopes of graphs, and root polytopes of semi-balanced digraphs, there is a large, natural class of dissections into unimodular simplices. These are such that the

Facets of Symmetric Edge Polytopes for Graphs with Few Edges

. Symmetric edge polytopes, also called adjacency polytopes, are lattice polytopes determined by simple undirected graphs. In this paper we study the number of facets of symmetric edge polytopes for

Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering

This work uses well-known Markov Chain Monte Carlo sampling methods to generate empirical evidence that for a fixed degree sequence, higher WattsStrogatz clustering in a connected graph corresponds to higher facet numbers in the associated symmetric edge polytope.



Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs

Let G be a connected bipartite graph with colour classes E and V and root polytope Q . Regarding the hypergraph H=(V,E) induced by G , we prove that the interior polynomial of H is equivalent to the

On the gamma-vector of symmetric edge polytopes

We study γ-vectors associated with h-vectors of symmetric edge polytopes both from a deterministic and a probabilistic point of view. On the deterministic side, we prove nonnegativity of γ2 for any


We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Grobner basis techniques, h

Root Polytopes and Growth Series of Root Lattices

The convex hull of the roots of a classical root lattice is called a root polytope. We determine explicit unimodular triangulations of the boundaries of the root polytopes associated to the root

A Characterization of the Tutte Polynomial via Combinatorial Embeddings

It is proved that the Tutte polynomial equals the generating function of spanning trees counted according to embedding-activities, which is, in fact, independent of the embedding.

A version of Tutte's polynomial for hypergraphs

Hypergraph polynomials and the Bernardi process

Recently O. Bernardi gave a formula for the Tutte polynomial $T(x,y)$ of a graph, based on spanning trees and activities just like the original definition, but using a fixed ribbon structure to order

Roots of Ehrhart polynomials arising from graphs

Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of the Ehrhart polynomials not merely supports the conjecture of Beck et al.

The h*-Polynomials of Locally Anti-Blocking Lattice Polytopes and Their γ-Positivity

A formula for the -polynomials of locally anti-blocking lattice polytopes is given and the -positivity ofh is discussed, which is unimodularly equivalent to an anti- blocking polytope by reflections of coordinate hyperplanes.