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Critical Sets in Latin Squares: An Intriguing Problem

โœ Scribed by Keedwell, A. Donald


Book ID
126875102
Publisher
The Mathematical Association
Year
2001
Tongue
English
Weight
215 KB
Volume
85
Category
Article
ISSN
0025-5572

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## 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

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A critical set C of order n is a partial latin square of order n which is uniquely completable to a latin square, and omitting any entry of the partial latin square destroys this property. The size s(C) of a critical set C is the number of filled cells in the partial latin square. The I size of a mi

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## Abstract Suppose that __L__ is a latin square of order __m__ and __P__โ€‰โŠ‘โ€‰__L__ is a partial latin square. If __L__ is the only latin square of order __m__ which contains __P__, and no proper subset of __P__ has this property, then __P__ is a __critical set__ of __L__. The critical set spectrum p