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Transversals in Row-Latin Rectangles

โœ Scribed by Arthur A. Drisko

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
258 KB
Volume
84
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

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 conjecture of Dillon on the existence of difference sets in groups of order 2 2s+2 with elementary abelian normal subgroups of order 2 s+1 .

๐Ÿ“œ SIMILAR VOLUMES

A Matroid Generalization of a Result on
A Matroid Generalization of a Result on Row-Latin Rectangles
โœ Glenn G. Chappell ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 194 KB

Let A be an m\_n matrix in which the entries of each row are all distinct. A. A. Drisko (1998, J. Combin. Theory Ser. A 84, 181 195) showed that if m 2n&1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in the

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โœ K. Balasubramanian ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 269 KB
Latin squares with restricted transversa
Latin squares with restricted transversals
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 **_

A result on generalized latin rectangles
A result on generalized latin rectangles
โœ Chai-Ling Deng; Chong-Keang Lim ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 396 KB

An alternative and simpler proof of the following result is given: Every r x s generalized partial latin rectangle Q on A = (1, 2, , k} can be extended to an n x n generalized latin square on A if and only if n 2 r + s -min{N(i) 1 i E A}, where N(i) denotes the number of times that the symbol i appe