Asymptotic enumeration of permutations avoiding generalized patterns
نویسندگان
چکیده
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...
متن کاملAsymptotic behaviour of permutations avoiding generalized patterns
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. Th...
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We give the first comprehensive collection of enumeration results for permutations that avoid barred patterns of length 6 4. We then use the method of prefix enumeration schemes to find recurrences counting permutations that avoid a barred pattern of length > 4 or a set of barred patterns.
متن کاملGenerating trees for permutations avoiding generalized patterns
We construct generating trees with with one and two labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, instead of inserting always the largest entry. This allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. W...
متن کاملPermutations Avoiding Arithmetic Patterns
A permutation π of an abelian group G (that is, a bijection from G to itself) will be said to avoid arithmetic progressions if there does not exist any triple (a, b, c) of elements of G, not all equal, such that c − b = b − a and π(c) − π(b) = π(b) − π(a). The basic question is, which abelian groups possess such a permutation? This and problems of a similar nature will be considered. 1 Notation...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2006
ISSN: 0196-8858
DOI: 10.1016/j.aam.2005.05.006