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Maximal sets of Latin squares and partial transversals

โœ Scribed by David A. Drake


Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
809 KB
Volume
1
Category
Article
ISSN
0378-3758

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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 **_

Completing Latin squares: Critical sets
โœ P. Horak; R. E. L. Aldred; H. Fleischner ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 135 KB

## Abstract It is shown that a critical set in a Latin square of order __n__โ‰ฅ8 has to have at least $\left \lfloor {4n-8}\over {3}\right\rfloor$ elements. ยฉ 2002 Wiley Periodicals, Inc. J Combin Designs 10: 419โ€“432, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1

Critical sets in nets and latin squares
โœ J.A. Cooper; T.P. McDonough; V.C. Mavron ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 911 KB
Completing Latin squares: Critical sets
โœ Peter Horak; Italo J. Dejter ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 96 KB

## Abstract It is shown that each critical set in a Latin square of order __n__โ€‰>โ€‰6 has to have at least $\left\lfloor {7n-\sqrt{n}-20}\over{2}\right\rfloor$ empty cells. ยฉ 2006 Wiley Periodicals, Inc. J Combin Designs 15: 77โ€“83, 2007