eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2019-10-02
vol. 21 no. 4
Combinatorics
10.23638/DMTCS-21-4-16
5438
journal article
Proofs of Conjectures about Pattern-Avoiding Linear Extensions
Colin Defant
After fixing a canonical ordering (or labeling) of the elements of a finite
poset, one can associate each linear extension of the poset with a permutation.
Some recent papers consider specific families of posets and ask how many linear
extensions give rise to permutations that avoid certain patterns. We build off
of two of these papers. We first consider pattern avoidance in $k$-ary heaps,
where we obtain a general result that proves a conjecture of Levin, Pudwell,
Riehl, and Sandberg in a special case. We then prove some conjectures that
Anderson, Egge, Riehl, Ryan, Steinke, and Vaughan made about pattern-avoiding
linear extensions of rectangular posets.
https://dmtcs.episciences.org/5438/pdf
Mathematics - Combinatorics
05A05, 05A15, 05A16