Transmutable λ-fold kite systems

Abstract

Informally, a G-design (X, B) is said to be ∈-transmutable into a G'-design (X, B') if we can take a set D_∈ = {∈_B : B ∈ B} of (isomorphic) edges, one from each copy of G, in such a way there exists a suitable bijection σ between B and D_∈ such that B' = {(B - ∈_B) + σ(B) : B ∈ B}. In the case that G is isomorphic to G' we say that the G-design is ∈-switchable. This paper determines the spectrum of λ-fold e-transmutable G-design where G is a kite (a triangle with an edge attached) and G' is either a kite or a 4-cycle.