A major index for matchings and set partitions
William Y. C Chen, Ira M. Gessel, Catherine H. Yan, Arthur L. B. Yang
Abstract
We introduce a statistic 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.
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