Euler-Mahonian Statistics On Ordered Set Partitions (II)

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Kasraoui, Anisse
Zeng, Jiang
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Abstract
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We study statistics on ordered set partitions whose generating functions are related to $p,q$-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of \stein (Arxiv:math.CO/0605670). Our basic idea is to encode ordered partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structure. We also give a partition version of MacMahon's theorem on the equidistribution of the statistics inversion number and major index on words.
Comment: 27 pages,8 figures
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Mathematics - Combinatorics, 05A15, 05A30
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