Applying the cluster method to count occurrences of generalized permutation patterns
نویسندگان
چکیده
منابع مشابه
Applying the Cluster Method to Count Occurrences of Generalized Permutation Patterns
Abstract. We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingŕımsson. In particular, we consider those patterns with three letters and one internal dash, as well as permutation statistics composed of counting the number of occurrences of multisets of such patterns...
متن کاملGeneralized Permutation Patterns — a Short Survey
An occurrence of a classical pattern p in a permutation π is a subsequence of π whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be required to be adjacent in the permutation. Subsets of permutations characterized by the avoidance—or the prescribed number of occurrences— of generalized patterns ...
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We study statistical properties of the random variables Xσ(π), the number of occurrences of the pattern σ in the permutation π. We present two contrasting approaches to this problem: traditional probability theory and the “less traditional” computational approach. Through the perspective of the first one, we prove that for any pair of patterns σ and τ , the random variables Xσ and Xτ are jointl...
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We consider two recent open problems stating that certain statistics on various sets of combinatorial objects are equidistributed. The first, posed by Anders Claesson and Svante Linusson, relates nestings in matchings on {1, 2, . . . , 2n} to occurrences of a certain pattern in permutations in Sn. The second, posed by Miles Jones and Jeffrey Remmel, relates occurrences of a large class of conse...
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2011
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236190903170706