We show that any affine block design D = (P, B) is a subset of a suitable commutative group G_D, with the property that a k-subset of P is a block of D if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design D is the group of automorphisms of G_D that leave P invariant. Whenever k is a prime p, G_D is an elementary abelian p-group.
|Number of pages||16|
|Journal||Journal of Algebraic Combinatorics|
|Publication status||Published - 2021|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics