A major index for matchings and set partitions

We introduce a statistic pmaj(P) for partitions of [n], and show that it is equidistributed with cr2, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj.

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: William Y. C. Chen, Ira M. Gessel, Catherine H. Yan, Arthur L. B. Yang
• Keywords: Block Elements, JCT 2008, Maximal Block Elements, Minimal Block Elements