Counting inversion sequences by parity successions and runs

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


Let In denote the set of inversion sequences of length n. In this paper, we enumerate members of In represented using positive integers according to parameters which track the number of runs and successions of letters of a given parity. To this end, we consider a four-parameter joint distribution on In and derive several general results for this distribution, providing further treatment of some particular cases. In order to prove our results, we make use of a non-standard generating function which allows for the system of recurrences satisfied by various refinements of the aforementioned joint distribution to be translated into a system of linear differential equations that can be solved explicitly. Finally, the more general problem of enumerating the members of In according to adjacencies involving two elements that are equivalent modulo m is considered.

Original languageEnglish
Pages (from-to)24-39
Number of pages16
JournalDiscrete Applied Mathematics
StatePublished - 15 May 2023

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.


  • Combinatorial statistic
  • Generating function
  • Inversion sequence
  • Parity succession

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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