By Martha Yip
Danilov, Karzanov and Koshevoy devised a combinatorial method to obtain regular unimodular triangulations of flow polytopes on acyclic directed graphs having a unique source and sink and with unit netflow. It was conjectured by González D'León et al. that the dual graph of a DKK triangulation has the structure of a lattice. Recently, proofs of the conjecture were announced independently by Bell and Ceballos, and by Berggren and Serhiyenko. We give another combinatorial approach towards the study of these lattices. I will discuss the combinatorics behind permutation flows and use them to obtain a formula for the h²-polynomial of the flow polytope (ie. a G-Eulerian polynomial). We then extend the concept of DKK triangulations to flow polytopes with nonnegative integer netflows and obtain a new proof of the generalized Lidskii formula for the volume of a flow polytope.
By Torsten Mütze
By Christian Stump
By Cyril Banderier
By Kilian Raschel
By Pierre-Vincent Koseleff
