Additivity of symmetric and subspace designs

Marco Buratti; Anamari Nakic

paper

Additivity of symmetric and subspace designs

arXiv:2307.08134

Abstract

A $2$ - $(v, k, λ)$ design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group $G$ in such a way that its block set is contained in (or coincides with) the set of all the zero-sum $k$ -subsets of $G$ . Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG $_{d} (n, q)$ , which was known to be additive only for $q = 2$ or $d = n - 1$ , is always established.