Resolving Triple Systems into Regular Configurations

Resolving Triple Systems into Regular Configurations

A λ − Triple System(v), or a λ–TS(V,B), is a pair (V, B) where V is a set and B is a subset of the 3-subsets of V so that every pair is in exactly λ elements of B. A regular configuration on p points with regularity ρ on l blocks is a pair (P,L) where L is a collection of 3-subsets of a (usually small) set P so that every p in P is in exactly ρ elements of L, and |L| = l. The Pasch configuratio...

Resolving P(v, 3, λ) designs into regular P3-configurations

There is one nontrivial regular configuration on two paths of three vertices, and one on three paths. Path designs which are resolvable into copies of these configurations are shown to exist whenever basic numerical conditions are met, with a few possible exceptions.

Configurations in Steiner triple systems

" Combinatorial Designs and their Applications " c 1999 (copyright owner as specified in the book).

Configurations and trades in Steiner triple systems

The main result of this paper is the determination of all pairwise nonisomorphic trade sets of volume at most 10 which can appear in Steiner triple systems. We also enumerate partial Steiner triple systems having at most 10 blocks as well as configurations with no points of degree 1 and tradeable configurations having at most 12 blocks.

Lambda-fold complete graph decompositions into perfect four-triple configurations