Symmetric edge polytopes and matching generating polynomials

Hidefumi Ohsugi, Akiyoshi Tsuchiya
2021 Combinatorial Theory  
Symmetric edge polytopes A G of type A are lattice polytopes arising from the root system A n and finite simple graphs G. There is a connection between A G and the Kuramoto synchronization model in physics. In particular, the normalized volume of A G plays a central role. In the present paper, we focus on a particular class of graphs. In fact, for any cactus graph G, we give a formula for the h * -polynomial of A G by using matching generating polynomials, where G is the suspension of G. This
more » ... ves also a formula for the normalized volume of A G . Moreover, via methods from chemical graph theory, we show that for any cactus graph G, the h * -polynomial of A G is real-rooted. Finally, we extend the discussion to symmetric edge polytopes of type B, which are lattice polytopes arising from the root system B n and finite simple graphs.
doi:10.5070/c61055371 fatcat:x3zfb4q45fanlca5wg7eegxsgm