Counting set partitions by the number of movable letters

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


A movable letter within a sequence belonging to a class is one that may be transposed with its predecessor while staying within the class. We consider in this paper the problem of counting finite set partitions by the number of movable letters in their canonical sequential representations. A further restricted count on the set (Formula presented.) of partitions of (Formula presented.) with k blocks is given wherein it is required that no two equal letters be transposed. Explicit formulas for the associated exponential generating functions and for the totals of the respective statistics over all members of (Formula presented.) are found. To establish several of our results, we solve explicitly various linear partial differential equations. Finally, some comparable results are found for the class of non-crossing partitions of (Formula presented.) where in this case we focus instead on the ordinary generating functions of the associated distributions.

Original languageEnglish
Pages (from-to)384-403
Number of pages20
JournalJournal of Difference Equations and Applications
Issue number3
StatePublished - 3 Mar 2020

Bibliographical note

Publisher Copyright:
© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.


  • Set partitions
  • combinatorial statistic
  • generating function
  • non-crossing partition

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


Dive into the research topics of 'Counting set partitions by the number of movable letters'. Together they form a unique fingerprint.

Cite this