Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns

David Callan, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


Recently, it has been determined that there are 242 Wilf classes of triples of 4-letter permutation patterns by showing that there are 32 non-singleton Wilf classes. Moreover, the generating function for each triple lying in a non-singleton Wilf class has been explicitly determined. In this paper, toward the goal of enumerating avoiders for the singleton Wilf classes, we obtain the generating function for all but one of the triples containing 1324. (The exceptional triple is conjectured to be intractable.) Our methods are both combinatorial and analytic, including generating trees, recurrence relations, and decompositions by left-right maxima. Sometimes this leads to an algebraic equation for the generating function, sometimes to a functional equation or a multi-index recurrence amenable to the kernel method.
Original languageEnglish
Pages (from-to)32-61
Number of pages30
JournalPure Mathematics and Applications
Issue number1
StatePublished - 2018


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