Karola Mészáros ; Alejandro H. Morales ; Brendon Rhoades - The polytope of Tesler matrices

dmtcs:2475 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2475
The polytope of Tesler matricesConference paper

Authors: Karola Mészáros 1; Alejandro H. Morales 2; Brendon Rhoades 3

We introduce the Tesler polytope Tesn(a), whose integer points are the Tesler matrices of size n with hook sums a1,a2,...,aninZ0. We show that Tesn(a) is a flow polytope and therefore the number of Tesler matrices is counted by the type An Kostant partition function evaluated at (a1,a2,...,an,ni=1ai). 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 Tesn(a) when all ai>0 is given by the Mahonian numbers and calculate the volume of Tesn(1,1,...,1) to be a product of consecutive Catalan numbers multiplied by the number of standard Young tableaux of staircase shape.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: Tesler matrices,flow polytopes,Kostant partition function,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • PostDoctoral Research Fellowship; Funder: National Science Foundation; Code: 1103933
  • Combinatorics and Representation Theory; Funder: National Science Foundation; Code: 1068861
  • Polytopes in Combinatorics and Algebra; Funder: National Science Foundation; Code: 1501059

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