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arXiv · 2405.12672

Small examples of mosaics of combinatorial designs

Vedran Krčadinac
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Abstract

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.

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Vedran Krčadinac. 2024-05-21. Small examples of mosaics of combinatorial designs. https://doi.org/10.1016/j.exco.2024.100163

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