Rise, Fall and Level Statistics on r-Jacobi-Stirling Set Partitions

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalJournal of Analysis & Number Theory
Issue number1
StatePublished - 2019


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