On the volume of a certain polytope
| dc.creator | Chan, Clara S. | |
| dc.creator | Robbins, David P. | |
| dc.creator | Yuen, David S. | |
| dc.date | 1998-10-27 | |
| dc.date | 1998-10-29 | |
| dc.date.accessioned | 2026-07-07T05:26:37Z | |
| dc.date.available | 2026-07-07T05:26:37Z | |
| dc.description | Let n >= 2 be an integer and consider the set T_n of n by n permutation matrices pi for which pi_{ij}=0 for j>=i+2. In this paper we study the convex hull of T_n, which we denote by P_n. P_n is a polytope of dimension binom{n}{2}. Our main purpose is to provide evidence for the following conjecture concerning its volume. Let v_n denote the minimum volume of a simplex with vertices in the affine lattice spanned by T_n. Then the volume of P_n is v_n times the product for i varying from 0 to n-2 of frac{1}{i+1} binom{2i}{i}. That is, P_n is the product of v_n and the first n-1 Catalan numbers. We also give a related result on the Ehrhart polynomial of P_n. | |
| dc.description | this version corrects a small number of typographical errors in the original | |
| dc.identifier | https://arxiv.org/abs/math/9810154 | |
| dc.identifier | http://arxiv.org/abs/math/9810154 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77613 | |
| dc.subject | Combinatorics | |
| dc.title | On the volume of a certain polytope | |
| dc.type | text |