Equivalence classes of mesh patterns with a dominating pattern
Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length. We provide sufficient conditions for coincidence of mesh patterns, when only permutations also avoiding a longer classical pattern ar...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2018-02-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3283/pdf |
| _version_ | 1827323783478771712 |
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| author | Murray Tannock Henning Ulfarsson |
| author_facet | Murray Tannock Henning Ulfarsson |
| author_sort | Murray Tannock |
| collection | DOAJ |
| description | Two mesh patterns are coincident if they are avoided by the same set of
permutations, and are Wilf-equivalent if they have the same number of avoiders
of each length. We provide sufficient conditions for coincidence of mesh
patterns, when only permutations also avoiding a longer classical pattern are
considered. Using these conditions we completely classify coincidences between
families containing a mesh pattern of length 2 and a classical pattern of
length 3. Furthermore, we completely Wilf-classify mesh patterns of length 2
inside the class of 231-avoiding permutations. |
| first_indexed | 2024-04-25T01:59:08Z |
| format | Article |
| id | doaj.art-fd69ac8e4e1443ae8f64aaf63a590f98 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:59:08Z |
| publishDate | 2018-02-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-fd69ac8e4e1443ae8f64aaf63a590f982024-03-07T15:33:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502018-02-01Vol. 19 no. 2, Permutation...Permutation Patterns10.23638/DMTCS-19-2-63283Equivalence classes of mesh patterns with a dominating patternMurray TannockHenning UlfarssonTwo mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length. We provide sufficient conditions for coincidence of mesh patterns, when only permutations also avoiding a longer classical pattern are considered. Using these conditions we completely classify coincidences between families containing a mesh pattern of length 2 and a classical pattern of length 3. Furthermore, we completely Wilf-classify mesh patterns of length 2 inside the class of 231-avoiding permutations.https://dmtcs.episciences.org/3283/pdfmathematics - combinatorics05a05, 05a15 |
| spellingShingle | Murray Tannock Henning Ulfarsson Equivalence classes of mesh patterns with a dominating pattern Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05a05, 05a15 |
| title | Equivalence classes of mesh patterns with a dominating pattern |
| title_full | Equivalence classes of mesh patterns with a dominating pattern |
| title_fullStr | Equivalence classes of mesh patterns with a dominating pattern |
| title_full_unstemmed | Equivalence classes of mesh patterns with a dominating pattern |
| title_short | Equivalence classes of mesh patterns with a dominating pattern |
| title_sort | equivalence classes of mesh patterns with a dominating pattern |
| topic | mathematics - combinatorics 05a05, 05a15 |
| url | https://dmtcs.episciences.org/3283/pdf |
| work_keys_str_mv | AT murraytannock equivalenceclassesofmeshpatternswithadominatingpattern AT henningulfarsson equivalenceclassesofmeshpatternswithadominatingpattern |