Subregularity in infinitely labeled generating trees of restricted permutations

Toufik Mansour, Reza Rastegar, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, we revisit the application of generating trees to the pattern avoidance problem for permutations. In particular, we study this problem for certain general sets of patterns and propose a new procedure leveraging the FinLabel algorithm and exploiting the subregularities in the associated generating trees. We consider some general kinds of generating trees for which the FinLabel algorithm fails to determine in a finite number of iterations the generating function that enumerates the underlying class of permutations. Our procedure provides a unified approach in these cases leading to a system of equations satisfied by a certain finite set of generating functions which can be readily solved with the aid of programming.

Original languageEnglish
Article number102393
JournalAdvances in Applied Mathematics
StatePublished - Sep 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.


  • Directed graph
  • Generating function
  • Generating tree
  • Pattern avoidance

ASJC Scopus subject areas

  • Applied Mathematics


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