10.23638/DMTCS-21-2-6
https://dmtcs.episciences.org/5350
Auli, Juan S.
Juan S.
Auli
Elizalde, Sergi
Sergi
Elizalde
Consecutive Patterns in Inversion Sequences
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 $i$.
Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck 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.
Comment: Final version to appear in DMTCS
episciences.org
Mathematics - Combinatorics
05A05 (Primary) 05A15, 05A19 (Secondary)
arXiv.org - Non-exclusive license to distribute
2019-11-04
2019-11-04
2019-11-04
eng
journal article
arXiv:1904.02694
10.48550/arXiv.1904.02694
1365-8050
10.48550/arxiv.1904.02694
https://dmtcs.episciences.org/5350/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 21 no. 2, Permutation Patters 2018
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