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Rise, Fall and Level Statistics on r-Jacobi-Stirling Set Partitions |
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PP: 1-8 |
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Author(s) |
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Toufik Mansour,
Mark Shattuck,
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Abstract |
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| In this paper, we consider sequential representations of the recently introduced r-Jacobi-Stirling set partitions (denoted by
P(n, k)) and study various statistics on these representations.We compute an explicit formula for the generating function which counts
members ofP(n, k) where k and r are fixed according to these statistics in the case of levels, descents and ascents. In each case, we use
a more-or-less uniform strategy which also yields the distribution of the statistic on those members ofP(n, k) ending in a certain letter.
Finally, we give explicit formulas for the total number of levels, descents and ascents within all of the members of P(n, k), providing
both algebraic and combinatorial proofs. |
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