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MiS Preprint
59/2018
Arithmetic aspects of symmetric edge polytopes
Akihiro Higashitani, Katharina Jochemko and Mateusz Michałek
We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gr\"obner 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 Gal’s conjecture for arbitrary flag unimodular triangulations in this case, and, beyond that, we prove a strengthening due to Nevo and Petersen (2011).
