منابع مشابه
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 ...
متن کاملAvoiding consecutive patterns in permutations
The number of permutations that do not contain, as a factor (subword), a given set of permutations Π is studied. A new treatment of the case Π = {12 · · · k} is given and then some numerical data is presented for sets Π consisting of permutations of length at most 4. Some large sets of Wilf-equivalent permutations are also given.
متن کاملPermutations 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...
متن کاملConsecutive 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...
متن کاملConsecutive Up-down Patterns in Up-down Permutations
In this paper, we study the distribution of the number of consecutive pattern matches of the five up-down permutations of length four, 1324, 2314, 2413, 1432, and 3412, in the set of up-down permutations. We show that for any such τ , the generating function for the distribution of the number of consecutive pattern matches of τ in the set of up-down permutations can be expressed in terms of wha...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2003
ISSN: 0196-8858
DOI: 10.1016/s0196-8858(02)00527-4