Some constructions for [formula omitted] pairwise orthogonal diagonal Latin squares based on difference matrices

R Julian R Abel,Yang Li

doi:10.1016/j.disc.2014.11.018

Some constructions for [formula omitted] pairwise orthogonal diagonal Latin squares based on difference matrices

R Julian R Abel, Yang Li

Open Access

https://doi.org/10.1016/j.disc.2014.11.018

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Journal: Discrete Mathematics	Publication Date: Dec 24, 2014
Citations: 1	License type: elsevier-specific: oa user license

Affiliation: UNSW Sydney, Soochow University

#Diagonal Latin Squares #Orthogonal Diagonal Latin Squares + Show 7 more

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Abstract

A diagonal Latin square is one whose main and back diagonals are both transversals. Difference matrices, quasi-difference matrices and holey quasi-difference matrices are used to construct t pairwise orthogonal diagonal Latin squares of order v (t PODLS(v)) in this paper. For t=3,4,5, known existence results for t PODLS(v) are then updated; for t=3, 4, and 5, there remain respectively 1, 11 and 32 unsolved cases, the largest of which are v=10, 54 and 98 respectively.

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