Asymptotic behaviour of permutations avoiding generalized patterns
نویسنده
چکیده
Visualizing permutations as labelled trees allows us to to specify restricted permutations, and to analyze their counting sequence. The asymptotic behaviour for permutations that avoid a given pattern is given by the Stanley-Wilf conjecture, which was proved by Marcus and Tardos in 2005. Another interesting question is the occurence of generalized patterns, i.e. patterns containing subwords. There are good asymptotic results for consecutive patterns and certain variations, but only specific results for patterns with subwords of length exactly 2. The goal of the project is to fully understand the analysis performed by Elizalde and Noy on such patterns, and to try to extend these results to other cases.
منابع مشابه
Asymptotic Enumeration of Permutations Avoiding Generalized Patterns
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be adjacent in an occurrence of the pattern in the permutation, and consecutive patterns are a particular case of them. We determine the asymptotic behavior of the n...
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