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- W19601023 abstract "We introduce the Tesler polytope Tes_n(a_1,a_2,...,a_n), whose integer points are the Tesler matrices of size n with nonnegative integer hook sums a_1,a_2,...,a_n. We show that Tes_n(a) is a flow polytope and therefore the number of Tesler matrices is counted by the type A_n Kostant partition function evaluated at (a_1,a_2,...,a_n,-a_1-...-a_n). We describe the faces of this polytope in terms of Tesler tableaux and characterize when the polytope is simple. We prove that the h-vector of Tes_n(a) when all a_i>0 is given by the Mahonian numbers and calculate the volume of Tes_n(1,1,...,1) to be a product of consecutive Catalan numbers multiplied by the number of standard Young tableaux of staircase shape." @default.
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- W19601023 date "2016-05-26" @default.
- W19601023 modified "2023-10-14" @default.
- W19601023 title "The polytope of Tesler matrices" @default.
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- W19601023 doi "https://doi.org/10.1007/s00029-016-0241-2" @default.
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