Permutations and words counted by consecutive patterns

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Permutations and words counted by consecutive patterns

Generating functions which count occurrences of consecutive sequences in a permutation or a word which matches a given pattern are studied by exploiting the combinatorics associated with symmetric functions. Our theorems take the generating function for the number of permutations which do not contain a certain pattern and give generating functions refining permutations by the both the total num...

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Consecutive patterns in permutations

In this paper we study the distribution of the number of occurrences of a permutation σ as a subword among all permutations in Sn. We solve the problem in several cases depending on the shape of σ by obtaining the corresponding bivariate exponential generating functions as solutions of certain linear differential equations with polynomial coefficients. Our method is based on the representation ...

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Avoiding consecutive patterns in permutations

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Consecutive patterns in permutations: clusters and generating functions

We use the cluster method in order to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite families of patterns of a given shape. Our main tool is the cluster method of Goulden and Jackson. We also prove some that, for a large class of patter...

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ژورنال

عنوان ژورنال: Advances in Applied Mathematics

سال: 2006

ISSN: 0196-8858

DOI: 10.1016/j.aam.2005.09.005