Counting occurrences of patterns in permutations

Autor:	Conway, Andrew R, Guttmann, Anthony J
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Computer Science - Data Structures and Algorithms 05A15 (Primary) 05A05 06-04 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 32 pages. Updated references from previous version. Removal on earlier discussion of Stieltjes sequences, which was incomplete and confusing
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.12682 Zobrazit plný text záznamu View this record from Arxiv