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arXiv · 1704.02701

Volumes of generalized Chan-Robbins-Yuen polytopes

Sylvie Corteel·Jang Soo Kim·Karola Mészáros
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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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Sylvie Corteel, Jang Soo Kim, Karola Mészáros. 2017-04-10. Volumes of generalized Chan-Robbins-Yuen polytopes. https://arxiv.org/abs/1704.02701

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