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 pa...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2019-11-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/5350/pdf |
| _version_ | 1827323741524197376 |
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| author | Juan S. Auli Sergi Elizalde |
| author_facet | Juan S. Auli Sergi Elizalde |
| author_sort | Juan S. Auli |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T01:57:22Z |
| format | Article |
| id | doaj.art-561bbde552614e4ca6de69edf7548e61 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:57:22Z |
| publishDate | 2019-11-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-561bbde552614e4ca6de69edf7548e612024-03-07T15:38:27ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502019-11-01Vol. 21 no. 2, Permutation...10.23638/DMTCS-21-2-65350Consecutive Patterns in Inversion SequencesJuan S. AuliSergi ElizaldeAn 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.https://dmtcs.episciences.org/5350/pdfmathematics - combinatorics05a05 (primary) 05a15, 05a19 (secondary) |
| spellingShingle | Juan S. Auli Sergi Elizalde Consecutive Patterns in Inversion Sequences Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05a05 (primary) 05a15, 05a19 (secondary) |
| title | Consecutive Patterns in Inversion Sequences |
| title_full | Consecutive Patterns in Inversion Sequences |
| title_fullStr | Consecutive Patterns in Inversion Sequences |
| title_full_unstemmed | Consecutive Patterns in Inversion Sequences |
| title_short | Consecutive Patterns in Inversion Sequences |
| title_sort | consecutive patterns in inversion sequences |
| topic | mathematics - combinatorics 05a05 (primary) 05a15, 05a19 (secondary) |
| url | https://dmtcs.episciences.org/5350/pdf |
| work_keys_str_mv | AT juansauli consecutivepatternsininversionsequences AT sergielizalde consecutivepatternsininversionsequences |