Speaker:  William Dugan, University of Massachusetts
Title: On the f-vector of flow polytopes for complete graphs
Time: 2:30 PM, Monday, November 18, 2024
Place:  Malott 206

Abstract: The Chan-Robbins-Yuen polytope ($CRY_n$) of order $n$ is a face of the Birkhoff polytope of doubly stochastic matrices that is also a flow polytope of the directed complete graph $K_{n+1}$ with netflow $(1,0,0, \ldots , 0, -1)$. The volume and lattice points of this polytope have been actively studied, however its face structure has been studied less. We give explicit formulas and generating functions for the $f$-vector of $CRY_n$ by using Hille's (2007) result bijecting faces of a flow polytope to certain graphs, as well as Andresen-Kjeldsen's (1976) result that enumerates certain subgraphs of the directed complete graph. We extend our results to flow polytopes over the complete graph having arbitrary (non-negative) netflow vectors and study the face lattice of $CRY_n$.


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