Avoiding a pair of patterns in multisets and compositions

Vít Jelínek, Toufik Mansour, José L. Ramírez, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, we study the Wilf-type equivalence relations among multiset permutations. We identify all multiset equivalences among pairs of patterns consisting of a pattern of length three and another pattern of length at most four. To establish our results, we make use of a variety of techniques, including Ferrers-equivalence arguments, sorting by minimal/maximal letters, analysis of active sites and direct bijections. In several cases, our arguments may be extended to prove multiset equivalences for infinite families of pattern pairs. Our results apply equally well to the Wilf-type classification of compositions, and as a consequence, we obtain a complete description of the Wilf-equivalence classes for pairs of patterns of type (3,3) and (3,4) on compositions, with the possible exception of two classes of type (3,4).

Original languageEnglish
Article number102286
Pages (from-to)102286
Number of pages1
JournalAdvances in Applied Mathematics
StatePublished - Feb 2022


  • Composition
  • Multiset
  • Pattern avoidance
  • Wilf-equivalence

ASJC Scopus subject areas

  • Applied Mathematics


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