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

Nathaniel Shar, Doron Zeilberger, Shalosh B. Ekhad

Publication date: 9 April 2015

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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