## Abstract

Looking at incidence matrices of t-(Formula presented.) designs as (Formula presented.) 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 (Formula presented.) 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 |
---|---|

Pages (from-to) | 85–95 |

Number of pages | 11 |

Journal | DESIGNS CODES AND CRYPTOGRAPHY |

Volume | 86 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2018 |

MoE publication type | A1 Journal article-refereed |

## Keywords

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