The polytope of Tesler matrices

• Karola Mészáros ^[1] ; Alejandro H. Morales ^[2] ; Brendon Rhoades ^[2]
  1. [1] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
  2. [2] University of California
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 425-454
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We introduce the Tesler polytope Tesn(a), whose integer points are the Tesler matrices of size n with hook sums a1, a2,..., an ∈ Z≥0. 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, −n i=1 ai). 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.