Set partitions and m-excedances

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, we consider a generalized m-excedance statistic on set partitions which is analogous to the usual excedance statistic on permutations when m = 0. We study it from a probabilistic perspective in which set partitions are regarded as geometrically distributed words satisfying a so-called restricted growth property. We derive a general set of recurrences satisfied by the relevant generating functions and, in the m = 0 and m = 1 cases, �find an explicit formula for the distribution of the statistic recording the number of m-excedances in partitions having a �fixed number of blocks. When m = 0, one can also determine the joint distribution for the number of excedances with the major index statistic on set partitions. Further recurrences may be given in this case as well as formulas for the mean number of excedances and the variance.
Original languageEnglish
Pages (from-to)42-54
Number of pages13
JournalNotes on Number Theory and Discrete Mathematics
Issue number1
StatePublished - 15 Jan 2016


Dive into the research topics of 'Set partitions and m-excedances'. Together they form a unique fingerprint.

Cite this