A major index for matchings and set partitions

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

A major index for matchings and set partitions

Combinatorics 2007-05-23 v1

Authors: William Y. C Chen , Ira M. Gessel , Catherine H. Yan , 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.

Keywords

partition theory permutations noncrossing partitions

Cite

@article{arxiv.math/0701096,
  title  = {A major index for matchings and set partitions},
  author = {William Y. C Chen and Ira M. Gessel and Catherine H. Yan and Arthur L. B. Yang},
  journal= {arXiv preprint arXiv:math/0701096},
  year   = {2007}
}

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17 pages, 9 figures

A major index for matchings and set partitions

Abstract

Keywords

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