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The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r

2015/04/09 by Shalosh B. Ekhad, Ekhad, Shalosh B., Nathaniel Shar +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1504.02513

5 pages

arxiv created 2015/04/09 · openalex publication_date 2015/04/09 · arxiv updated 2015/04/13 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We use the Robinson-Schensted correspondence, followed by symbol-crunching, in order to derive explicit expressions for the quantities mentioned in the title. We follow it by number crunching, in order to compute the first terms of these sequences. As an encore, we cleverly implement Ira Gessel's celebrated determinant formula for the generating functions of these sequences, to crank out many terms. This modest tribute is dedicated to one of the greatest enumerators alive today (and definitely the most modest one!), Ira Martin Gessel, who is turning 64 years-old today

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