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Статья

Counting vertices in Gelfand-Zetlin polytopes

Journal of Combinatorial Theory, Series A. 2013. Vol. 120. P. 960-969.

We discuss the problem of counting vertices in Gelfand--Zetlin polytopes. Namely, we deduce a partial differential equation with constant coefficients on the exponential generating function for these numbers. For some particular classes of Gelfand-Zetlin polytopes, the number of vertices can be given by explicit formulas.