Volumes of generalized Chan-Robbins-Yuen polytopes

2017/04/10 by Corteel, Sylvie, Kim, Jang Soo, Mészáros, Karola
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.02701

Abstract

The normalized volume of the Chan-Robbins-Yuen polytope (CRY_n) is the product of consecutive Catalan numbers. The polytope CRY_n has captivated combinatorial audiences for over a decade, as there is no combinatorial proof for its volume formula. In their quest to understand CRY_n better, the third author and Morales introduced two natural generalizations of it and conjectured that their volumes are certain powers of 2 multiplied by a product of consecutive Catalan numbers. Zeilberger proved one of these conjectures. In this paper we present proofs of both conjectures.

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