Associated Permutations of Complete Non-Ambiguous Trees
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909158094143488 |
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| author | Chen, Daniel Ohlig, Sebastian |
| author_facet | Chen, Daniel Ohlig, Sebastian |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11117 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Associated Permutations of Complete Non-Ambiguous Trees Chen, Daniel Ohlig, Sebastian Combinatorics 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. |
| title | Associated Permutations of Complete Non-Ambiguous Trees |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2210.11117 |