Classification Of Uniform Flag Triangulations Of The Boundary Of The Full Root Polytope Of Type A

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Abstract

The full root polytope of type A is the convex hull of all pairwisedifferences of the standard basis vectors which we represent by forward andbackward arrows. We completely classify all flag triangulations of this polytopethat are uniform in the sense that the edges may be described as a function ofthe relative order of the indices of the four basis vectors involved. These fifteentriangulations fall naturally into three classes: three in the lex class, three in therevlex class and nine in the Simion class. We also consider a refined face countwhere we distinguish between forward and backward arrows. We prove the refinedface counts only depend on the class of the triangulations. The refined face generatingfunctions are expressed in terms of the Catalan and Delannoy generatingfunctions and the modified Bessel function of the first kind.

Original languageEnglish
Pages (from-to)462-511
Number of pages50
JournalActa Mathematica Hungarica
Volume163
Issue number2
DOIs
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2020, Akadémiai Kiadó, Budapest, Hungary.

Keywords

  • Bessel function
  • Catalan number
  • Delannoy number
  • cyclohedron
  • face vector
  • flag complex
  • matching ensemble
  • type B associahedron

ASJC Scopus subject areas

  • General Mathematics

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