Prolific permutations and permuted packings: downsets containing many large patterns

Research output: Contribution to journalArticle

A permutation of n letters is k-prolific if each (n - k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific permutations for each k, proving that k-prolific permutations of m letters exist for every m >= k^2/2+2k+1, and that none exist of smaller size. Key to these results is a natural bijection between k-prolific permutations and certain "permuted" packings of diamonds.
Original languageEnglish
Pages (from-to)98-121
Number of pages24
JournalJournal of Combinatorial Theory Series A
Volume153
Early online date1 Sep 2017
DOIs
StateE-pub ahead of print - 1 Sep 2017

    Research areas

  • permutation, pattern, pattern poset, downset, prolific permutation, packing, permuted packing

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