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 language | English |
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Pages (from-to) | 1470-1479 |
Number of pages | 10 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - 2016 |
Bibliographical note
Publisher Copyright:Copyright © by SIAM.
Keywords
- Eulerian
- Generating functions
- Lecture hall
- Triangulations
ASJC Scopus subject areas
- General Mathematics