Abstract
The existence of edge-coloured block designs with block size four is studied for all nonisomorphic colourings of the edges of a K4. There are 25 nonisomorphic edge-coloured K4's; for each, we examine the existence of edge-coloured designs with the minimum possible index. Uniform cases lead to block designs, perpendicular arrays, nested Steiner triple systems, idempotent Schroeder quasigroups, and other combinatorial objects.
Original language | English (US) |
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Pages (from-to) | 230-245 |
Number of pages | 16 |
Journal | Aequationes Mathematicae |
Volume | 36 |
Issue number | 2-3 |
DOIs | |
State | Published - Jun 1988 |
Externally published | Yes |
Keywords
- AMS (1980) subject classification: Primary 05B30
ASJC Scopus subject areas
- General Mathematics
- Discrete Mathematics and Combinatorics
- Applied Mathematics