Simplifying modular lattices by removing doubly irreducible elements
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908319003705344 |
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| author | Kohonen, Jukka |
| author_facet | Kohonen, Jukka |
| contents | Lattices are simplified by removing some of their doubly irreducible elements, resulting in smaller lattices called racks. All vertically indecomposable modular racks of $n \le 40$ elements are listed, and the numbers of all modular lattices of $n \le 40$ elements are obtained by Pólya counting. SageMath code is provided that allows easy access both to the listed racks, and to the modular lattices that were not listed. More than 3000-fold savings in storage space are demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simplifying modular lattices by removing doubly irreducible elements Kohonen, Jukka Combinatorics Discrete Mathematics 06C05 (Primary) 05C30, 20B25 (Secondary) G.2.1; G.2.2 Lattices are simplified by removing some of their doubly irreducible elements, resulting in smaller lattices called racks. All vertically indecomposable modular racks of $n \le 40$ elements are listed, and the numbers of all modular lattices of $n \le 40$ elements are obtained by Pólya counting. SageMath code is provided that allows easy access both to the listed racks, and to the modular lattices that were not listed. More than 3000-fold savings in storage space are demonstrated. |
| title | Simplifying modular lattices by removing doubly irreducible elements |
| topic | Combinatorics Discrete Mathematics 06C05 (Primary) 05C30, 20B25 (Secondary) G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2311.16643 |