Counting Occurrences of Patterns in Permutations

We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and the general behaviour of these is reasonably well-known. We s...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 32; no. 1
Main Authors Conway, Andrew, Guttmann, Anthony
Format Journal Article
LanguageEnglish
Published 17.01.2025
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Summary:We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and the general behaviour of these is reasonably well-known. We slightly extend some of the known results in that case, and exhaustively study the case of patterns of length 4, about which there is little previous knowledge. For such patterns, there are seven Wilf classes, and based on extensive enumerations and careful series analysis, we have conjectured the asymptotic behaviour for all classes.
ISSN:1077-8926
1077-8926
DOI:10.37236/12963