## Abstract It is shown that a critical set in a Latin square of order __n__โฅ8 has to have at least $\left \lfloor {4n-8}\over {3}\right\rfloor$ elements. ยฉ 2002 Wiley Periodicals, Inc. J Combin Designs 10: 419โ432, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1
Critical sets in nets and latin squares
โ 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
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract It is shown that each critical set in a Latin square of order __n__โ>โ6 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: 77โ83, 2007
## Abstract Suppose that __L__ is a latin square of order __m__ and __P__โโโ__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
## 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