On the number of faces of Gelfand-Zetlin polytopes
arXiv:1705.07074 · doi:10.1090/spmj/1714
Abstract
We obtain a recurrence relation for the f-polynomial of Gelfand-Zetlin polytopes by analyzing geometric properties of a linear projection of the Gelfand-Zetlin polytope onto a cube. We apply this recurrence relation to find explicit formulas for the f-polynomials and h-polynomials of Gelfand-Zetlin polytopes that belong to several simplest one-parameter families.
19 pages, 5 figures, in Russian. Added motivations in introduction, removed computational details from some examples, removed subsection "Gelfand--Zetlin simplexes" (the referee said that it is well-known)