Séminaire Lotharingien de Combinatoire, B78b (2018), 8 pp.

James Haglund and Emily Sergel

A Generalized Major Index Statistic on Tableaux

Abstract. We extend the family of statistics maj_d, introduced for permutations by Kadell [J. Combin. Theory, Ser.~A, 40(1):22--44, 1985], to standard Young tableaux. At one extreme, we have the traditional major index statistic maj,sub>1 for tableaux. At the other end, whenever N >= n-1, then maj_N = inv, the inversion statistic introduced by Haglund and Stevens [Sém. Lothar. Combin., 56:B56c, 2006]. This answers a question of Assaf [Sém. Lothar. Combin., 60:B60c, 2008], who defined maj₂ and maj₃ for tableaux.

Received: September 18, 2017. Accepted: March 11, 2018.

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