Pasch Decompositions of Lambda-Fold Triple Systems

Peter Adams1, Elizabeth J. Billington1, C. A. Rodger2
1Centre for Combinatorics Department of Mathematics The University of Queensland Queensland 4072 Australia
2Department of Discrete and Statistical Sciences 120 Mathematics Annex Auburn University Auburn, Alabama U.S.A. 36849-5307

Abstract

We find the set of integers \(v\) for which \(\lambda K_v\) may be decomposed into sets of four triples forming Pasch configurations, for all \(\lambda\). We also remove the remaining exceptional values of \(v\) for decomposing \(K_v\) into sets of other four-triple configurations.