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2014

Permutations avoiding 1324 and patterns in {\L}ukasiewicz paths

Bevan, David

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The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets.

By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81.
This improves on a previous lower bound of 9.47.
Central to our proof is an examination of the asymptotic distributions of certain substructures in the Hasse graphs of the permutations.

Permutations avoiding 1324 and patterns in {\L}ukasiewicz paths · Around

Built on

String overlaps, pattern matching, and nontransitive games
L. J. Guibas and A. M. Odlyzko · 1981
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Systems of functional equations
Michael Drmota · 1997
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Combinatorial Enumeration
Ian P. Goulden and David M. Jackson · 2004
Earlier work this paper cites.
Excluded permutation matrices and the Stanley-Wilf conjecture
Adam Marcus and Gábor Tardos · 2004
Earlier work this paper cites.
On the Stanley-Wilf limit of 4231-avoiding permutations and a conjecture of Arratia
M. H. Albert, M. Elder, A. Rechnitzer, P. Westcott, and M. Zabrocki · 2006
Earlier work this paper cites.

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