Proof of a Conjecture of Chan, Robbins, and Yuen

TL;DR

This paper proves a conjecture relating the volume of a high-dimensional polytope to the product of Catalan numbers, using the Morris Constant Term Identity, thus confirming a recent mathematical hypothesis.

Contribution

It provides a proof of a conjecture connecting polytope volume with Catalan numbers, employing the Morris Constant Term Identity, which was previously unverified.

Findings

Confirmed the conjecture about polytope volume and Catalan numbers

Demonstrated the application of the Morris Constant Term Identity in geometric combinatorics

Established a link between high-dimensional polytopes and classical combinatorial sequences

Abstract

Using the celebrated Morris Constant Term Identity, we deduce a recent conjecture of Chan, Robbins, and Yuen (math.CO/9810154), that asserts that the volume of a certain $n(n-1)/2$-dimensional polytope is given by the product of the first n-1 Catalan numbers.