On product formulas for volumes of flow polytopes

Abstract

We outline the construction of a family of polytopes pm,n, indexed by m ∈ℤ≥0 and n ∈ℤ≥2, whose volumes are given by the product (Formula presented) The Chan-Robbins-Yuen polytope CRYn, whose volume is (Formula presented), coincides with p0,n-1. Our construction of the polytopes pm,n is an application of a systematic method we develop for expressing volumes of a class of flow polytopes as the number of certain triangular arrays. The latter is also the constant term of a formal Laurent series.