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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.18274 |
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| _version_ | 1866914581316632576 |
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| author | Muller, Thomas |
| author_facet | Muller, Thomas |
| contents | Higher dimensional permutations are tuples of d-1 permutations that can be identified with a point set in a d-dimensional grid. In N. Bonichon and P.-J. Morel, {\it J. Integer Sequences} 25 (2022), several conjectures regarding the enumeration of pattern avoiding d-permutations were stated.
In this paper, we consider a mapping from d-permutations to $2^{d-1}-$ary trees that naturally generalizes the classical max-tree construction for permutations. We then show that, when restricted to d-permutations avoiding (21,12) and 231, this mapping yields a bijection with d-ary trees. This result resolves one of the conjectures of Bonichon and Morel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18274 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Max-tree for d-permutations and pattern avoidance Muller, Thomas Combinatorics Higher dimensional permutations are tuples of d-1 permutations that can be identified with a point set in a d-dimensional grid. In N. Bonichon and P.-J. Morel, {\it J. Integer Sequences} 25 (2022), several conjectures regarding the enumeration of pattern avoiding d-permutations were stated. In this paper, we consider a mapping from d-permutations to $2^{d-1}-$ary trees that naturally generalizes the classical max-tree construction for permutations. We then show that, when restricted to d-permutations avoiding (21,12) and 231, this mapping yields a bijection with d-ary trees. This result resolves one of the conjectures of Bonichon and Morel. |
| title | Max-tree for d-permutations and pattern avoidance |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.18274 |