Upper bounds for the Stanley–Wilf limit of 1324 and other layered patterns

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Claesson, Anders and Jelínek, Vít and Steingrimsson, Einar (2012) Upper bounds for the Stanley–Wilf limit of 1324 and other layered patterns. Journal of Combinatorial Theory Series A, 119 (8). pp. 1680-1691. ISSN 0097-3165 (https://doi.org/10.1016/j.jcta.2012.05.006)

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Abstract

We prove that the Stanley-Wilf limit of any layered permutation pattern of length l is at most 4l(2), and that the Stanley-Wilf limit of the pattern 1324 is at most 16. These bounds follow from a more general result showing that a permutation avoiding a pattern of a special form is a merge of two permutations, each of which avoids a smaller pattern. We also conjecture that, for any k >= 0, the set of 1324-avoiding permutations with k inversions contains at least as many permutations of length n + 1 as those of length n. We show that if this is true then the Stanley-Wilf limit for 1324 is at most e(pi root 2/3) similar or equal to 13.001954.

ORCID iDs

Claesson, Anders ORCID logoORCID: https://orcid.org/0000-0001-5797-8673, Jelínek, Vít and Steingrimsson, Einar ORCID logoORCID: https://orcid.org/0000-0003-4611-0849;
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