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

Title: On the Stanley–Wilf limit of 4231-avoiding permutations and a conjecture of Arratia
Creator: Albert, M. H.; Elder, Murray; Rechnitzer, A.; Westcott, P.; Zabrocki, M.
Relation: Advances in Applied Mathematics Vol. 36, Issue 2, p. 96-105
Publisher Link: http://dx.doi.org/10.1016/j.aam.2005.05.007
Publisher: Academic Press
Resource Type: journal article
Date: 2006
Description: We show that the Stanley–Wilf limit for the class of 4231-avoiding permutations is at least by 9.47. 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 Stanley–Wilf limit of a class of permutations avoiding a single permutation of length k cannot exceed (k−1)2. The result is established by constructing a sequence of finite automata that accept subclasses of the class of 4231-avoiding permutations and analysing their transition matrices.
Subject: permutation classes; Automata
Identifier: http://hdl.handle.net/1959.13/928094
Identifier: uon:10341
Identifier: ISSN:0196-8858
Language: eng
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