Mosaics of combinatorial designs

Oliver Wilhelm Gnilke*, Marcus Greferath, Mario Osvin Pavčević

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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 languageEnglish
Pages (from-to)85–95
Number of pages11
JournalDESIGNS CODES AND CRYPTOGRAPHY
Volume86
Issue number1
DOIs
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

Keywords

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

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