Associated Permutations of Complete Non-Ambiguous Trees
We explore new connections between complete non-ambiguous trees (CNATs) and permutations. We give a bijection between tree-like tableaux and a specific subset of CNATs. This map is used to establish and solve a recurrence relation for the number of tree-like tableaux of a fixed size without occupied...
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| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2024-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | http://dmtcs.episciences.org/11169/pdf |
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| author | Daniel Chen Sebastian Ohlig |
| author_facet | Daniel Chen Sebastian Ohlig |
| author_sort | Daniel Chen |
| collection | DOAJ |
| description | We explore new connections between complete non-ambiguous trees (CNATs) and permutations. We give a bijection between tree-like tableaux and a specific subset of CNATs. This map is used to establish and solve a recurrence relation for the number of tree-like tableaux of a fixed size without occupied corners, proving a conjecture by Laborde-Zubieta. We end by establishing a row/column swapping operation on CNATs and identify new areas for future research. |
| format | Article |
| id | doaj-art-da61c19e3a3044cfa433dace460d2e1e |
| institution | OA Journals |
| issn | 1365-8050 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj-art-da61c19e3a3044cfa433dace460d2e1e2025-08-20T01:49:32ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502024-04-01vol. 25:2Combinatorics10.46298/dmtcs.1116911169Associated Permutations of Complete Non-Ambiguous TreesDaniel ChenSebastian OhligWe explore new connections between complete non-ambiguous trees (CNATs) and permutations. We give a bijection between tree-like tableaux and a specific subset of CNATs. This map is used to establish and solve a recurrence relation for the number of tree-like tableaux of a fixed size without occupied corners, proving a conjecture by Laborde-Zubieta. We end by establishing a row/column swapping operation on CNATs and identify new areas for future research.http://dmtcs.episciences.org/11169/pdfmathematics - combinatorics |
| spellingShingle | Daniel Chen Sebastian Ohlig Associated Permutations of Complete Non-Ambiguous Trees Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics |
| title | Associated Permutations of Complete Non-Ambiguous Trees |
| title_full | Associated Permutations of Complete Non-Ambiguous Trees |
| title_fullStr | Associated Permutations of Complete Non-Ambiguous Trees |
| title_full_unstemmed | Associated Permutations of Complete Non-Ambiguous Trees |
| title_short | Associated Permutations of Complete Non-Ambiguous Trees |
| title_sort | associated permutations of complete non ambiguous trees |
| topic | mathematics - combinatorics |
| url | http://dmtcs.episciences.org/11169/pdf |
| work_keys_str_mv | AT danielchen associatedpermutationsofcompletenonambiguoustrees AT sebastianohlig associatedpermutationsofcompletenonambiguoustrees |