## Abstract

Looking at incidence matrices of t-(v,k,λ) designs as v× b matrices with two 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× 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.

Original language | English |
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Journal | Designs, Codes, and Cryptography |

Volume | 86 |

Issue number | 1 |

Pages (from-to) | 85-95 |

Number of pages | 11 |

ISSN | 0925-1022 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Externally published | Yes |

## Keywords

- Affine plane
- c-Mosaic
- Resolvable design
- t-Design