Five subsets of permutations enumerated as weak sorting permutations

David Callan, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


In this paper, we show that the number of members of Sn avoiding any one
of five specific triples of 4-letter patterns is given by sequence A111279, which is known to count weak sorting permutations. By numerical evidence, there are no other (nontrivial) triples of 4-letter patterns giving rise to this sequence. We make use of a variety of methods [5, 6] in proving our result, including recurrences, the kernel method, direct counting, and bijections.
Original languageEnglish
Pages (from-to)327-340
Number of pages14
JournalSoutheast Asian Bulletin of Mathematics
Issue number3
StatePublished - 2018


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