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On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia

M. H. Albert·M. Elder·A. Rechnitzer·P. Westcott·M. Zabrocki
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Abstract

We construct a sequence of finite automata that accept subclasses of the class of 4231-avoiding permutations. We thereby show that the Wilf-Stanley limit for the class of 4231-avoiding permutations is bounded below by 9.35. This bound shows that this class has the largest such limit among all classes of permutations avoiding a single permutation of length 4 and refutes the conjecture that the Wilf-Stanley limit of a class of permutations avoiding a single permutation of length k cannot exceed (k-1)^2.

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M. H. Albert, M. Elder, A. Rechnitzer, P. Westcott, M. Zabrocki. 2005-02-23. On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia. https://doi.org/10.1016/j.aam.2005.05.007

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