Existence of orthogonal Latin squares with aligned subsquares

DOI10.1016/0012-365X(86)90070-1zbMath0591.05010OpenAlexW1991897317WikidataQ56688015 ScholiaQ56688015MaRDI QIDQ1074586

B. George

Publication date: 1986

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(86)90070-1

zbMATH Keywords

aligned subsquareorthogonal latin squares

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items (24)

Constructions of doubly resolvable Steiner quadruple systems ⋮ Orthogonal trades and the intersection problem for orthogonal arrays ⋮ Incomplete conjugate orthogonal idempotent Latin squares ⋮ On the existence of incomplete transversal designs with block size five ⋮ Triangulations of 3-way regular tripartite graphs of degree 4, with applications to orthogonal latin squares ⋮ Self-orthogonal Mendelsohn triple systems ⋮ Incomplete idempotent Schröder quasigroups and related packing designs ⋮ Supports of indecomposable \(B(4,2;v)\) designs ⋮ Embedding partial Latin squares in Latin squares with many mutually orthogonal mates ⋮ On elementary, odd, semimagic and other classes of antilattices ⋮ Constructions of pairs of orthogonal latin cubes ⋮ The existence of skew Howell designs of side 2n and order \(2n+2\) ⋮ Further results on incomplete (3,2,1)-conjugate orthogonal idempotent Latin squares ⋮ A polynomial embedding of pairs of orthogonal partial Latin squares ⋮ Existence of frame SOLS of type \(a^nb^1\) for odd \(n\) ⋮ Generalized Steiner systems GS4 (2, 4, v, g) for g = 2, 3, 6 ⋮ Embeddings on \(S(2,4,v)\) ⋮ Incomplete self-orthogonal latin squares \(ISOLS(6m+6,2m)\) exist for all m ⋮ Partial graph design embeddings and related problems ⋮ Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results ⋮ Mutually orthogonal Latin squares with large holes ⋮ Constructions of Nested Orthogonal Arrays ⋮ Two-dimensional balanced sampling plans avoiding adjacent units ⋮ Howell designs with sub-designs

Cites Work

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• Orthogonal Latin squares with subsquares
• Orthogonal latin squares with orthogonal subsquares
• A general construction for group-divisible designs
• More mutually orthogonal latin squares
• Sub-Latin squares and incomplete orthogonal arrays
• On the spectra of certain types of latin square
• Mols with holes
• Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture

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