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A major index for matchings and set partitions

2007/01/03 by William Y. C. Chen, William Y. C Chen, Ira M. Gessel +6
Computer Science · Mathematics · #05A15 #05A18 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #math.CO #msc:05A15 #msc:05A18

paper · pdf · doi:10.48550/arxiv.math/0701096

17 pages, 9 figures

arxiv created 2007/01/03 · openalex publication_date 2007/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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