An inversion sequence of length $n$ is a sequence of integers $e=e_1\cdots e_n$ which satisfies for each $i\in[n]=\{1,2,\ldots,n\}$ the inequality $0\le e_i < i$. For a set of patterns $P$, we let $\mathbf{I}_n(P)$ denote the set of inversion sequences of length $n$ that avoid all the patterns from~$P$. We say that two sets of patterns $P$ and $Q$ are I-Wilf-equivalent if $|\mathbf{I}_n(P)|=|\mathbf{I}_n(Q)|$ for every~$n$. In this paper, we show that the number of I-Wilf-equivalence classes among triples of length-3 patterns is $137$, $138$ or~$139$. In particular, to show that this number is exactly $137$, it remains to prove $\{101,102,110\}\stackrel{\mathbf{I}}{\sim}\{021,100,101\}$ and $\{100,110,201\}\stackrel{\mathbf{I}}{\sim}\{100,120,210\}$.
@article{10_37236_11603,
author = {David Callan and V{\'\i}t Jel{\'\i}nek and Toufik Mansour},
title = {Inversion sequences avoiding a triple of patterns of 3 letters},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {3},
doi = {10.37236/11603},
zbl = {1519.05003},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11603/}
}
TY - JOUR
AU - David Callan
AU - Vít Jelínek
AU - Toufik Mansour
TI - Inversion sequences avoiding a triple of patterns of 3 letters
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/11603/
DO - 10.37236/11603
ID - 10_37236_11603
ER -
%0 Journal Article
%A David Callan
%A Vít Jelínek
%A Toufik Mansour
%T Inversion sequences avoiding a triple of patterns of 3 letters
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/11603/
%R 10.37236/11603
%F 10_37236_11603
David Callan; Vít Jelínek; Toufik Mansour. Inversion sequences avoiding a triple of patterns of 3 letters. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11603
