Lattices with exponentially large kissing numbers
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866917791022448640 |
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| author | Vlăduţ, Serge |
| author_facet | Vlăduţ, Serge |
| contents | We construct a sequence of lattices $\{L_{n_i}\subset \mathbb R^{n_i}\}$ for $n_i\longrightarrow\infty$, with exponentially large kissing numbers, namely, $\log_2τ(L_{n_i})> 0.0338\cdot n_i -o(n_i)$. We also show that the maximum lattice kissing number $ τ^l_{n}$ in $n$ dimensions verifies $\log_2τ^l_{n}> 0.0219\cdot n -o(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_00886 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Lattices with exponentially large kissing numbers Vlăduţ, Serge Number Theory Algebraic Geometry Combinatorics Metric Geometry 11H31, 11H71, 14G15, 52C17 We construct a sequence of lattices $\{L_{n_i}\subset \mathbb R^{n_i}\}$ for $n_i\longrightarrow\infty$, with exponentially large kissing numbers, namely, $\log_2τ(L_{n_i})> 0.0338\cdot n_i -o(n_i)$. We also show that the maximum lattice kissing number $ τ^l_{n}$ in $n$ dimensions verifies $\log_2τ^l_{n}> 0.0219\cdot n -o(n)$. |
| title | Lattices with exponentially large kissing numbers |
| topic | Number Theory Algebraic Geometry Combinatorics Metric Geometry 11H31, 11H71, 14G15, 52C17 |
| url | https://arxiv.org/abs/1802.00886 |