# Ehrhart theory of symmetric edge polytopes via ribbon structures

@inproceedings{Kalman2022EhrhartTO, title={Ehrhart theory of symmetric edge polytopes via ribbon structures}, author={Tam'as K'alm'an and Lilla T'othm'er'esz}, year={2022} }

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.

## 3 Citations

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

- Mathematics
- 2022

. 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

- Mathematics
- 2022

. 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

- Mathematics
- 2022

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.

## References

SHOWING 1-10 OF 14 REFERENCES

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

- Mathematics
- 2016

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

- Mathematics
- 2022

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…

### ARITHMETIC ASPECTS OF SYMMETRIC EDGE POLYTOPES

- MathematicsMathematika
- 2019

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

- MathematicsSIAM J. Discret. Math.
- 2011

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

- Mathematics, Computer Science
- 2006

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.

### Hypergraph polynomials and the Bernardi process

- Mathematics
- 2018

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

- Mathematics
- 2011

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

- MathematicsDiscret. Comput. Geom.
- 2021

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.