$2\times 2$ monotone grid classes are finitely based
In this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain $2 \times 2$ (generalized) grid classes having two monotone cells in the same...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2016-02-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/1325/pdf |
| _version_ | 1797270073316999168 |
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| author | Michael Albert Robert Brignall |
| author_facet | Michael Albert Robert Brignall |
| author_sort | Michael Albert |
| collection | DOAJ |
| description | In this note, we prove that all $2 \times 2$ monotone grid classes are
finitely based, i.e., defined by a finite collection of minimal forbidden
permutations. This follows from a slightly more general result about certain $2
\times 2$ (generalized) grid classes having two monotone cells in the same row. |
| first_indexed | 2024-04-25T01:58:28Z |
| format | Article |
| id | doaj.art-5d09f452e5a945ddad7fcada609b97c9 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:58:28Z |
| publishDate | 2016-02-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-5d09f452e5a945ddad7fcada609b97c92024-03-07T15:30:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502016-02-01Vol. 18 no. 2, Permutation...Permutation Patterns10.46298/dmtcs.13251325$2\times 2$ monotone grid classes are finitely basedMichael AlbertRobert BrignallIn this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain $2 \times 2$ (generalized) grid classes having two monotone cells in the same row.https://dmtcs.episciences.org/1325/pdfmathematics - combinatorics05a05 |
| spellingShingle | Michael Albert Robert Brignall $2\times 2$ monotone grid classes are finitely based Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05a05 |
| title | $2\times 2$ monotone grid classes are finitely based |
| title_full | $2\times 2$ monotone grid classes are finitely based |
| title_fullStr | $2\times 2$ monotone grid classes are finitely based |
| title_full_unstemmed | $2\times 2$ monotone grid classes are finitely based |
| title_short | $2\times 2$ monotone grid classes are finitely based |
| title_sort | 2 times 2 monotone grid classes are finitely based |
| topic | mathematics - combinatorics 05a05 |
| url | https://dmtcs.episciences.org/1325/pdf |
| work_keys_str_mv | AT michaelalbert 2times2monotonegridclassesarefinitelybased AT robertbrignall 2times2monotonegridclassesarefinitelybased |