Additivity of affine designs

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3 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)755-770
Number of pages16
JournalJournal of Algebraic Combinatorics
Volume53
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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