Additivity of affine designs

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We show that any affine block design D = (P, B) is a subset of a suitable commutativegroup G_D, with the property that a k-subset of P is a block of D if and only if its kelements sum up to zero. As a consequence, the group of automorphisms of any affinedesign D is the group of automorphisms of G_D that leave P invariant. Whenever k isa prime p, G_D is an elementary abelian p-group.
Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Algebraic Combinatorics
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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