## 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: 419β432, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1
Completing Latin squares: Critical sets II
β Scribed by Peter Horak; Italo J. Dejter
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 96 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
It is shown that each critical set in a Latin square of order nβ>β6 has to have at least $\left\lfloor {7n-\sqrt{n}-20}\over{2}\right\rfloor$ empty cells. Β© 2006 Wiley Periodicals, Inc. J Combin Designs 15: 77β83, 2007
π SIMILAR VOLUMES
We show that any partial 3r Γ3r Latin square whose filled cells lie in two disjoint r Γr sub-squares can be completed. We do this by proving the more general result that any partial 3r by 3r Latin square, with filled cells in the top left 2r Γ 2r square, for which there is a pairing of the columns s
## Abstract Suppose that __L__ is a latin square of order __m__ and __P__βββ__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