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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 maj_{2} and maj_{3} for tableaux.

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

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