Arithmetic aspects of symmetric edge polytopes

Akihiro Higashitani, Katharina Jochemko, and Mateusz Michałek

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Submission date: 23. Jul. 2018
published in: Mathematika : a journal of pure and applied mathematics, 65 (2019) 3, p. 763-784 
DOI number (of the published article): 10.1112/S0025579319000147
Bibtex
MSC-Numbers: 05A15, 52B1
Keywords and phrases: Symmetric edge polytope, h^∗ -polynomial, real roots
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gröbner basis techniques, half-open decompositions and methods for interlacing polynomials we provide an explicit formula for the h-polynomial in case of complete bipartite graphs. In particular, we show that the h-polynomial is gamma-positive and real-rooted. This proves Gals conjecture for arbitrary flag unimodular triangulations in this case, and, beyond that, we prove a strengthening due to Nevo and Petersen (2011).