## Yan, Chunyan and Lin, Zhicong - Inversion sequences avoiding pairs of patterns

dmtcs:5964 - Discrete Mathematics & Theoretical Computer Science, June 29, 2020, vol. 22 no. 1 - https://doi.org/10.23638/DMTCS-22-1-23
Inversion sequences avoiding pairs of patterns

Authors: Yan, Chunyan and Lin, Zhicong

The enumeration of inversion sequences avoiding a single pattern was initiated by Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck independently. Their work has sparked various investigations of generalized patterns in inversion sequences, including patterns of relation triples by Martinez and Savage, consecutive patterns by Auli and Elizalde, and vincular patterns by Lin and Yan. In this paper, we carried out the systematic study of inversion sequences avoiding two patterns of length $3$. Our enumerative results establish further connections to the OEIS sequences and some classical combinatorial objects, such as restricted permutations, weighted ordered trees and set partitions. Since patterns of relation triples are some special multiple patterns of length $3$, our results complement the work by Martinez and Savage. In particular, one of their conjectures regarding the enumeration of $(021,120)$-avoiding inversion sequences is solved.

Volume: vol. 22 no. 1
Section: Combinatorics
Published on: June 29, 2020
Submitted on: December 11, 2019
Keywords: Mathematics - Combinatorics