The Spectrum of Dihedral Quadruple Systems

摘要

An ordered analogue of quadruple systems QS(υ, λ)s is dihedral quadruple systems (DQS). A DQS(υ, λ) is a pair (S, T) where S is a finite set and τ is a family of dihedral quadruples of elements of S called blocks, such that every ordered triple of distinct elements of S belongs to exactly λ blocks of τ. When λ = 1, Stojakovic solved the spectrum problem of DQS(υ, 1). It is proved that a DQS(υ, λ) exists if and only if λυ(υ - 1)(υ-2) ≡ 0 (mod 8).