Combinatorics

Summary.

• equivalence between designs and (multi)graph colouring/decomposition problem

• necessary conditions for a BIBD

• construction methods for designs

• Wilson's Theorem

• Fisher's Inequality

• Important definitions:

  • design

  • blocks

  • balanced, regular, uniform

  • BIBD

  • complementary design

  • difference collection

• Notation:

  • \(b\text{,}\) \(v\text{,}\) \(r\text{,}\) \(k\text{,}\) \(\lambda\)