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For a permutation $\pi$, let $S_{n}(\pi)$ be the number of permutations on $n$ letters avoiding $\pi$.
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M. H. Albert, M. Elder, A. Rechnitzer, P. Westcott, and M. Zabrocki, On the Stanley-Wilf limit of 4231-avoiding permutations and a conjecture of Arratia, Adv. in Appl. Math
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M. Bóna, A new upper bound for 1324-avoiding permutations, preprint, arXiv:1207.2379
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E. Steingrímsson, Some open problems on permutation patterns, in: Surveys in combinatorics 2013, London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 2013, 239–263
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S. Guillemot and D. Marx, Finding Small Patterns in Permutations in Linear Time, Proc. SODA 2014
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