On the number of faces of the Gelfand–Zetlin polytope

Melikhova, E.

doi:10.1090/spmj/1714

On the number of faces of the Gelfand–Zetlin polytope
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by E. V. Melikhova
Translated by: A. Zhukova

St. Petersburg Math. J. 33 (2022), 553-568

DOI: https://doi.org/10.1090/spmj/1714

Published electronically: May 5, 2022

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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 $f$-polynomial of the polytope. This recurrence relation is applied to finding the $f$-polynomials and $h$-polynomials for one-parameter families of Gelfand–Zetlin polytopes of simplest types.

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