COUNTING SUBWORD PATTERNS IN PERMUTATIONS ARISING AS FLATTENED PARTITIONS OF SETS

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review

Abstract

We consider various statistics on the set Fn consisting of the distinct permutations of length n+1 that arise as a flattening of some partition of the same size. In particular, we enumerate members of Fn according to the number of occurrences of three-letter consecutive patterns, considered more broadly in the context of r-partitions. As special cases of our results, we obtain formulas for the number of members of Fn avoiding a given consecutive pattern and for the total number of occurrences of a pattern over all members of Fn

Original languageEnglish
Pages (from-to)146-177
Number of pages32
JournalApplicable Analysis and Discrete Mathematics
Volume16
Issue number1
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022. Applicable Analysis and Discrete Mathematics.All Rights Reserved.

Keywords

  • Combinatorial statistic
  • Flattened partition
  • Kernel method
  • Pattern avoidance
  • Subword

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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