A major index for matchings and set partitions

Details A major index for matchings and set partitions A major index for matchings and set partitions

2007-01-03

arxiv.org/abs/math/0701096v1

Mathematics

Combinatorics

17 pages, 9 figures

Scientific paper

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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