A major index for matchings and set partitions

William Y. C Chen; Ira M. Gessel; Catherine H. Yan; Arthur L. B. Yang

paper

A major index for matchings and set partitions

arXiv:math/0701096

Abstract

We introduce a statistic $\pmaj$ on partitions of $[n] = {1, 2, ..., n}$ , and show that it is equidistributed with the number of 2-crossings over 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 inversion number and major index.

17 pages, 9 figures