A Major Index for Matchings and Set Partitions

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

  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.

  AMS Classification:   05A18, 05A15


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