episciences.org_5350_1669548810
1669548810
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
11
04
2019
Vol. 21 no. 2, Permutation...
Consecutive Patterns in Inversion Sequences
Juan S.
Auli
Sergi
Elizalde
An inversion sequence of length $n$ is an integer sequence $e=e_{1}e_{2}\dots
e_{n}$ such that $0\leq e_{i}<i$ for each $i$.
CorteelMartinezSavageWeselcouch and MansourShattuck began the study of
patterns in inversion sequences, focusing on the enumeration of those that
avoid classical patterns of length 3. We initiate an analogous systematic study
of consecutive patterns in inversion sequences, namely patterns whose entries
are required to occur in adjacent positions. We enumerate inversion sequences
that avoid consecutive patterns of length 3, and generalize some results to
patterns of arbitrary length. Additionally, we study the notion of Wilf
equivalence of consecutive patterns in inversion sequences, as well as
generalizations of this notion analogous to those studied for permutation
patterns. We classify patterns of length up to 4 according to the corresponding
Wilf equivalence relations.
11
04
2019
5350
https://arxiv.org/licenses/nonexclusivedistrib/1.0
arXiv:1904.02694
10.48550/arXiv.1904.02694
https://arxiv.org/abs/1904.02694v2
https://arxiv.org/abs/1904.02694v1
10.23638/DMTCS2126
https://dmtcs.episciences.org/5350

https://dmtcs.episciences.org/5856/pdf