About the determinant of complete non-ambiguous trees
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908135242858496 |
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| author | Aval, Jean-Christophe |
| author_facet | Aval, Jean-Christophe |
| contents | Complete non-ambiguous trees (CNATs) are combinatorial objects which appear in various contexts.Recently, Chen and Ohlig studied the notion of permutations associated to these objects, and proposed a series of nice conjectures.Most of them were proved by Selig and Zhu, through a connection with the abelian sandpile model.But one conjecture remained open, about the distribution of a natural statistic named determinant.We prove this conjecture, in a bijective way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11951 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | About the determinant of complete non-ambiguous trees Aval, Jean-Christophe Combinatorics Complete non-ambiguous trees (CNATs) are combinatorial objects which appear in various contexts.Recently, Chen and Ohlig studied the notion of permutations associated to these objects, and proposed a series of nice conjectures.Most of them were proved by Selig and Zhu, through a connection with the abelian sandpile model.But one conjecture remained open, about the distribution of a natural statistic named determinant.We prove this conjecture, in a bijective way. |
| title | About the determinant of complete non-ambiguous trees |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.11951 |