On the number of faces of the Gelfand–Zetlin polytope

Abstract

The combinatorics of the Gelfand–Zetlin polytope is studied. Geometric properties of a linear projection of this polytope onto a cube are employed to derive a recurrence relation for the f f -polynomial of the polytope. This recurrence relation is applied to finding the f f -polynomials and h h -polynomials for one-parameter families of Gelfand–Zetlin polytopes of simplest types.