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

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

2005-02-23

arxiv.org/abs/math/0502504v1

Advances in Applied Mathematics 36(2) Special Issue on Pattern Avoiding Permutations (2006) pages 96-105

Mathematics

Combinatorics

Submitted to Advances in Applied Mathematics

Scientific paper

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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