Séminaire Lotharingien de Combinatoire, B56c (2006), 15 pp.

Jim Haglund and Laura Stevens

An Extension of the Foata Map to Standard Young Tableaux

Abstract. We define an inversion statistic on standard Young tableaux. We prove that this statistic has the same distribution over SYT(\lambda) as the major index statistic by exhibiting a bijection on SYT(\lambda) in the spirit of the Foata map on permutations.

Received: July 17, 2006. Revised: October 31, 2006. Accepted: November 5, 2006. Final version: November 11, 2006.

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