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Critical sets in nets and latin squares

โœ Scribed by J.A. Cooper; T.P. McDonough; V.C. Mavron


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
911 KB
Volume
41
Category
Article
ISSN
0378-3758

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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

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## Abstract A critical set is a partial latin square that has a unique completion to a latin square, and is minimal with respect to this property. Let __scs__(__n__) denote the smallest possible size of a critical set in a latin square of order __n__. We show that for all __n__, $scs(n)\geq n\lfloo