It is shown that given an odd prime p, the number of even latin squares of order p+1 is not equal to the number of odd latin squares of order p+1. This result is a special case of a conjecture of Alon and Tarsi and has implications for various other combinatorial problems, including conjectures of R
The Effect of Categorization on Balanced Incomplete Blocks and Latin Squares
β Scribed by J. C. W. Rayner; G. F. Liddell; A. J. Seyb
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 670 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0323-3847
No coin nor oath required. For personal study only.
β¦ Synopsis
Robustness in the various analysis of variance models should be assessed with regard to all the assumptions. Here we assess the etTect of the continuity assumption. The models considered were chosen because they are in a sense fragile, and the elTects might be anticipated to be more dramatic here. We identify at least one of the balanced incomplete block models for which severe categorization leads to tests with unacceptable sizes and aberrant power curves. Otherwise most of the models examined are generally satisfactory -that is, robust with respect to the continuity assumption.
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## 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
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