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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| Published in | The Electronic journal of combinatorics Vol. 32; no. 1 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
17.01.2025
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| Online Access | Get full text |
| ISSN | 1077-8926 1077-8926 |
| DOI | 10.37236/12963 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Conway, Andrew Guttmann, Anthony |
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| Title | Counting Occurrences of Patterns in Permutations |
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