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On the \(f\)-vectors of Gelfand-Cetlin polytopes. (English) Zbl 1378.52010
Summary: A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so called the face structure of a ladder diagram. Using our description, we obtain a partial differential equation whose solution is the exponential generating function of \(f\)-vectors of GC-polytopes. This solves the open problem (2) posed by P. Gusev et al. [J. Comb. Theory, Ser. A 120, No. 4, 960–969 (2013; Zbl 1315.52009)].

MSC:
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
52B11 \(n\)-dimensional polytopes
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