Two generalizations of the metamorphosis definition

Let B(k, λ) be the spectrum of integers n such that there exists a Sλ(2, k, n), a balanced incomplete block design of order n, block size k and index λ. Lindner and Rosa [6] introduced the definition of a Sλ(2, 4, n) having a metamorphosis into a Sλ(2, 3, n) and proved that the necessary condition n ∈ B(3, λ) ∩B(4, λ) is also sufficient. The aim of this paper is to present two different generalizations of Lindner and Rosa’s idea in order to consider metamorphoses of Sλ(2, 4, n) for n ∈ B(4, λ) and n 6∈ B(3, λ). AMS classification: 05B05.