On the number of faces of Gelfand-Zetlin polytopes
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.
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