Combinatorial Designs
Block designs, Latin squares, and Steiner systems.
Combinatorial Designs. Block designs, Latin squares, and Steiner systems.
Foundations and canonical references
The standard treatments of combinatorial designs approach the subject from complementary angles. Colbourn, Handbook of Combinatorial Designs (2006) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Beth, Design Theory (1999) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for combinatorial designs include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2006Handbook of Combinatorial Designscolbourn-2006, dinitz-2006
- textbook · primary · 1999Design Theorybeth-1999, jungnickel-1999, lenz-1999
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