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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.22385 |
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| _version_ | 1866914586244939776 |
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| author | Hopkins, Sam |
| author_facet | Hopkins, Sam |
| contents | In this note, we introduce two $t$-analogues $I_n(q,t)$ and $\widetilde{I}_n(q,t)$ of the tree inversion enumerator $I_n(q)$. Although similar, $I_n(q,t)$ and $\widetilde{I}_n(q,t)$ are different. But they both seem to have interesting properties. In particular, we conjecture that their $q=-1$ specializations give two different, natural refinements of the zigzag numbers counting alternating permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two $t$-analogues of the tree inversion enumerator Hopkins, Sam Combinatorics In this note, we introduce two $t$-analogues $I_n(q,t)$ and $\widetilde{I}_n(q,t)$ of the tree inversion enumerator $I_n(q)$. Although similar, $I_n(q,t)$ and $\widetilde{I}_n(q,t)$ are different. But they both seem to have interesting properties. In particular, we conjecture that their $q=-1$ specializations give two different, natural refinements of the zigzag numbers counting alternating permutations. |
| title | Two $t$-analogues of the tree inversion enumerator |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.22385 |