Steiner Trades That Give Rise to Completely Decomposable Latin Interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial configuration it is possible to identify a subset which uniquely determines the structure of the configuration and in some cases is minimal with respect to this property. For example such subsets can be found by studying the literature on critical sets in latin squares (see Donovan and Howse [2]) and defining sets in block designs (see Street [7]), as well as in the study of premature partial latin squares (see Brankovic, Horak, Miller and Rosa [1]). Research has shown that computer analysis of critical sets, defining sets and premature partial latin squares is computationally expensive. This fact has led to a study of the inherent nature of the configuration in order to obtain information for refining searches and associat...

• Type: Journal
• Year: 2002
• Where: IJCM
• Authors: Richard Bean, Diane Donovan, Abdollah Khodkar, Anne Penfold Street
• Keywords: Critical Sets, IJCM 2002, Latin Squares, Partial Latin Squares