Small examples of mosaics of combinatorial designs
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arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908562285920256 |
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| author | Krčadinac, Vedran |
| author_facet | Krčadinac, Vedran |
| contents | We give the first example of a mosaic of three combinatorial designs with distinct parameters $2$-$(13,3,1)$, $2$-$(13,4,2)$, and $2$-$(13,6,5)$. Furthermore, we give examples of mosaics of $2$-$(9,3,2)$ designs that are not resolvable, thereby answering a question posed by M. Wiese and H. Boche. Finally, we give an example of a mosaic of projective planes of order $3$ that cannot be obtained by tiling groups with difference sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small examples of mosaics of combinatorial designs Krčadinac, Vedran Combinatorics 05B20, 05B05 We give the first example of a mosaic of three combinatorial designs with distinct parameters $2$-$(13,3,1)$, $2$-$(13,4,2)$, and $2$-$(13,6,5)$. Furthermore, we give examples of mosaics of $2$-$(9,3,2)$ designs that are not resolvable, thereby answering a question posed by M. Wiese and H. Boche. Finally, we give an example of a mosaic of projective planes of order $3$ that cannot be obtained by tiling groups with difference sets. |
| title | Small examples of mosaics of combinatorial designs |
| topic | Combinatorics 05B20, 05B05 |
| url | https://arxiv.org/abs/2405.12672 |