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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2404.03897 |
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| _version_ | 1866910399507464192 |
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| author | Matsuo, Atsushi Shimakura, Hiroki |
| author_facet | Matsuo, Atsushi Shimakura, Hiroki |
| contents | A series of integral lattices parametrised by integers $k,m,n$ are introduced and investigated, where $n$ is the rank of the lattice, including the root lattices described in a uniform way and unimodular lattices such as the Niemeier lattices of type $A_{24}$ and $D_{24}$. The lattices are characterised by means of a sublattice isomorphic to the root lattice of type $A_{n-1}$. A sufficient condition for existence of an orthogonal $k$-frame of such a lattice is given in terms of symmetric $2$-designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Checkerboard Lattices Matsuo, Atsushi Shimakura, Hiroki Combinatorics Primary 11H06, Secondary 17B22 A series of integral lattices parametrised by integers $k,m,n$ are introduced and investigated, where $n$ is the rank of the lattice, including the root lattices described in a uniform way and unimodular lattices such as the Niemeier lattices of type $A_{24}$ and $D_{24}$. The lattices are characterised by means of a sublattice isomorphic to the root lattice of type $A_{n-1}$. A sufficient condition for existence of an orthogonal $k$-frame of such a lattice is given in terms of symmetric $2$-designs. |
| title | Generalised Checkerboard Lattices |
| topic | Combinatorics Primary 11H06, Secondary 17B22 |
| url | https://arxiv.org/abs/2404.03897 |