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.
@article{10_37236_12963,
author = {Andrew Conway and Anthony Guttmann},
title = {Counting occurrences of patterns in permutations},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {1},
doi = {10.37236/12963},
zbl = {1556.05004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12963/}
}
TY - JOUR
AU - Andrew Conway
AU - Anthony Guttmann
TI - Counting occurrences of patterns in permutations
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/12963/
DO - 10.37236/12963
ID - 10_37236_12963
ER -
%0 Journal Article
%A Andrew Conway
%A Anthony Guttmann
%T Counting occurrences of patterns in permutations
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/12963/
%R 10.37236/12963
%F 10_37236_12963
Andrew Conway; Anthony Guttmann. Counting occurrences of patterns in permutations. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/12963
