A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote patterns in which the relative order of some of the letters does not matter. This paper elucidates connections between the avoidance sets of a few POPs with other combinatorial objects, directly answering five open questions posed by Gao and Kitaev in 2019. This was done by thoroughly analysing the avoidance sets and developing recursive algorithms to derive these sets and their corresponding combinatorial objects in parallel, which yielded natural bijections. We also analysed an avoidance set whose simple permutations are enumerated by the Fibonacci numbers and derived an algorithm to obtain them recursively.
@article{10_37236_10206,
author = {Kai Ting Keshia Yap and David Wehlau and Imed Zaguia},
title = {Permutations avoiding certain partially-ordered patterns},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {3},
doi = {10.37236/10206},
zbl = {1470.05012},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10206/}
}
TY - JOUR
AU - Kai Ting Keshia Yap
AU - David Wehlau
AU - Imed Zaguia
TI - Permutations avoiding certain partially-ordered patterns
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10206/
DO - 10.37236/10206
ID - 10_37236_10206
ER -
%0 Journal Article
%A Kai Ting Keshia Yap
%A David Wehlau
%A Imed Zaguia
%T Permutations avoiding certain partially-ordered patterns
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10206/
%R 10.37236/10206
%F 10_37236_10206
Kai Ting Keshia Yap; David Wehlau; Imed Zaguia. Permutations avoiding certain partially-ordered patterns. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10206
