A Major Index for Matchings and Set Partitions
Vincent Y. B. Chen, Ira M. Gessel, Catherine H. Yan and Arthur L.B. Yang
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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. Keywords: Download: Pdf |