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Some new row-complete Latin squares

✍ Scribed by D.S Archdeacon; J.H Dinitz; D.R Stinson; T.W Tillson


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
173 KB
Volume
29
Category
Article
ISSN
0097-3165

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In this article it is shown how to construct a row-complete latin square of order mn, given one of order m and given a sequencing of a group of order n. This yields infinitely many new orders for which row-complete latin squares can be constructed.

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A construction for a row-complete latin square of order n, where n is any odd composite number other than 9, is given in this article. Since row-complete latin squares of order 9 and of even order have previously been constructed, this proves that row-complete latin squares of every composite order

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

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