The homology torsion growth of determinantal hypertrees
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918464708411392 |
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| author | Mészáros, András |
| author_facet | Mészáros, András |
| contents | Fix a dimension $d\ge 2$, and let $T_n$ be a random $d$-dimensional determinantal hypertree on $n$ vertices. We prove that \[\frac{\log|H_{d-1}(T_n,\mathbb{Z})|}{n\choose {d}}\] converges in probability to a constant $c_d$, which satisfies
\[\frac{1}2 \log\left(\frac{d+1}e\right)\le c_d\le \frac{1}2 \log\left(d+1\right) .\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The homology torsion growth of determinantal hypertrees Mészáros, András Combinatorics Algebraic Topology Probability Fix a dimension $d\ge 2$, and let $T_n$ be a random $d$-dimensional determinantal hypertree on $n$ vertices. We prove that \[\frac{\log|H_{d-1}(T_n,\mathbb{Z})|}{n\choose {d}}\] converges in probability to a constant $c_d$, which satisfies \[\frac{1}2 \log\left(\frac{d+1}e\right)\le c_d\le \frac{1}2 \log\left(d+1\right) .\] |
| title | The homology torsion growth of determinantal hypertrees |
| topic | Combinatorics Algebraic Topology Probability |
| url | https://arxiv.org/abs/2506.14694 |