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On transversals in latin squares

โœ Scribed by K. Balasubramanian


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
269 KB
Volume
131
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES


Latin squares with restricted transversa
โœ Judith Egan; Ian M. Wanless ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 149 KB

## Abstract We prove that for all odd **__m__**โ‰ฅ**3** there exists a latin square of order 3 **__m__** that contains an (**__m__**โˆ’**1**) ร— **__m__** latin subrectangle consisting of entries not in any transversal. We prove that for all even **__n__**โ‰ฅ**10** there exists a latin square of order **_

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It is shown that an m\_n row-latin rectangle with symbols in [1, 2, ..., k], k n, has a transversal whenever m 2n&1, and that this lower bound for m is sharp. Several applications are given. One is the construction of mappings which are generalizations of complete mappings. Another is the proof of a

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A simple expression for triples of signs of group Latin squares is given; in particular we prove that it depends only on the order.