2014/07/19 by Trent G. Marbach, Trent Gregory Marbach, Marbach, Trent Gregory
Decision Sciences · Engineering · Mathematics · #05B15 #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #graph theory and CDMA systems #math.CO #msc:05B15
paper · pdf · doi:10.48550/arxiv.1407.5174
24 pages
openalex publication_date 2014/07/19 · arxiv created 2015/03/16 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A paper by Cavenagh and Wanless diagnosed the possible intersection of any two transversals of the back circulant Latin square Bn, and used the result to completely determine the spectrum for 2-way k-homogeneous latin trades. We give a generalization of this problem for the intersection of μtransversals of Bn and provide a construction for this problem, as well as providing base designs for the construction in the cases μ= 3, 4 found by a computational search. This result is then applied to the problem of finding μ-way k-homogeneous Latin trades. We generalize this problem to the intersection of μtransversals of Bn such that the transversals intersect stably (that is, the intersection of any pair of transversals is independent of the choice of the pair) and show that these structures can be used to construct μ-way k-homogeneous circulant latin trades of odd order. We provide a number of basic existence and non-existence results for μtransversals of Bn that intersect stably, as well as the results of a computational search for small n. This is followed by the principal results of this paper; a construction that covers a large portion of the spectrum when n is sufficiently large, which requires certain base designs. These base designs are provided in the cases μ= 3,4, which were found by a computational search. We use this result to find the existence of μ-way k-homogeneous circulant latin trades of odd order, for μ= 3, 4.