Generating functions and triangulations for lecture hall cones

Matthias Beck, Benjamin Braun, Matthias Köppe, Carla D. Savage, Zafeirakis Zafeirakopoulos

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We investigate the arithmetic-geometric structure of the lecture hall cone Ln := {∈ ℝn : 0 ≤ 1/1 ≤ 2/1 ≤ 3/1 ≤ ...≤ n/n}. We show that Ln is isomorphic to the cone over the lattice pyramid of a reflexive simplex whose Ehrhart h-polynomial is given by the (n-1)st Eulerian polynomial and prove that lecture hall cones admit regular, flag, unimodular triangulations. After explicitly describing the Hilbert basis for Ln, we conclude with observations and a conjecture regarding the structure of unimodular triangulations of Ln, including connections between enumerative and algebraic properties of Ln and cones over unit cubes.

Original languageEnglish
Pages (from-to)1470-1479
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Volume30
Issue number3
DOIs
StatePublished - 2016

Bibliographical note

Publisher Copyright:
Copyright © by SIAM.

Keywords

  • Eulerian
  • Generating functions
  • Lecture hall
  • Triangulations

ASJC Scopus subject areas

  • Mathematics (all)

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