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arXiv · 1503.01643

Mosaics of Combinatorial Designs

Oliver W. Gnilke·Marcus Greferath·Mario Osvin Pavčević
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Abstract

Looking at incidence matrices of $t$-$(v,k,\lambda)$ designs as $v \times b$ matrices with $2$ possible entries, each of which indicates incidences of a $t$-design, we introduce the notion of a $c$-mosaic of designs, having the same number of points and blocks, as a matrix with $c$ different entries, such that each entry defines incidences of a design. In fact, a $v \times b$ matrix is decomposed in $c$ incidence matrices of designs, each denoted by a different colour, hence this decomposition might be seen as a tiling of a matrix with incidence matrices of designs as well. These mosaics have applications in experiment design when considering a simultaneous run of several different experiments. We have constructed infinite series of examples of mosaics and state some probably non-trivial open problems. Furthermore we extend our definition to the case of $q$-analogues of designs in a meaningful way.

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Oliver W. Gnilke, Marcus Greferath, Mario Osvin Pavčević. 2015-03-05. Mosaics of Combinatorial Designs. https://arxiv.org/abs/1503.01643

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