On permutations avoiding partially ordered patterns defined by bipartite graphs

TL;DR

This paper explores permutations avoiding certain partially ordered patterns defined by bipartite graphs, providing new enumeration results and characterizing Wilf-equivalence for specific pattern classes.

Contribution

It extends known results by offering general and specific enumerative formulas for POPs in permutations defined via bipartite graphs, including a complete characterization of Wilf-equivalence for N-shape posets.

Findings

Enumerative formulas for POPs defined by bipartite graphs

Complete characterization of Wilf-equivalence for N-shape patterns

Extension of known results in pattern avoidance literature

Abstract

Partially ordered patterns (POPs) generalize the notion of classical patterns studied in the literature in the context of permutations, words, compositions and partitions. In this paper, we give a number of general, and specific enumerative results for POPs in permutations defined by bipartite graphs, substantially extending the list of known results in this direction. In particular, we completely characterize the Wilf-equivalence for patterns defined by the N-shape posets.