Poset Pattern-Avoidance Problems Posed by Yakoubov

TL;DR

This paper extends Yakoubov's work by enumerating pattern-avoiding linear extensions of comb posets, resolving open problems, and proving her conjectures, advancing understanding in poset pattern-avoidance.

Contribution

It provides new enumeration results for pattern-avoiding linear extensions of comb posets and confirms several of Yakoubov's unresolved conjectures.

Findings

Resolved many of Yakoubov's open problems.

Proved both conjectures from Yakoubov's paper.

Enumerated linear extensions avoiding certain length-3 patterns.

Abstract

Extending the work of Yakoubov, we enumerate the linear extensions of comb posets that avoid certain length-$3$ patterns. We resolve many of Yakoubov's open problems and prove both of the conjectures from her paper.