C.C. Lindner

The Flower Intersection Problem for Steiner Triple Systems

Abstract We determine here those pairs (k, v) for which there exist a pair of Steiner triple systems on the same u-set, the triples in one system containing a particular point are the same as those in the other system containing that point, and the two systems otherwise have exactly k triples in common. The obvious necessary conditions are sufficient, with two exceptions (k, v) = (1,9) and (4,9).

Maximum packings of uniform group divisible triple systems

Necessary and sufficient conditions are given for the existence of a maximum packing of K with triangles with all possible minimal leaves. This is of course equivalent to a maximum packing of a group divisible triple system with n groups of size m.

A Note on One-Factorizations Having a Prescribed Number of Edges in Common

Publisher Summary This chapter presents a note on one-factorizations having a prescribed number of edges in common. A 1-factor of the finite set V is just a set of 2-element subsets of V which partition V . In the chapter, the 2-element subsets of V will be called “edges.” A l-factorization is a pair ( V, F ) where V is a finite set and F is a collection of 1-factors of V , which partition ( v/2) , the set of all edges of V . F is a 1-factorization of V . The number | V | is called the “order of the 1-factorization ( V , F ),” and the spectrum for 1-factorizations is precisely the set of all even positive integers. The chapter presents a complete solution to the intersection problem for 1-factorization. The chapter explains the sets J [ υ ] for small υ.

A Few More Bibd's with k = 6 and λ = 1

Abstract W.H. Mills has shown that there exists a BIBD (v,6,l) for all v ≡ 1 or 6 (modulo 15), v > 36, with 165 possible exceptions. We show that such designs exist for 35 of these values.

Nathan Saul Mendelsohn

Publisher Summary This chapter reviews the background of Nathan Saul Mendelsohn. Nathan Mendelsohns contributions to mathematics in Canada as a teacher, administrator, editor, international delegate, “server-on-committees,” elected officer, board member, and moving force in general are well-known. The history of Mendelsohn triple systems is typical of Nathans work—that is, he has pioneered many avenues of research in combinatorics. Nathan is a remarkable mathematician in the two ways that really count: depth of scholarship and perception of the future.