Let A be an m\_n matrix in which the entries of each row are all distinct. A. A. Drisko (1998, J. Combin. Theory Ser. A 84, 181 195) showed that if m 2n&1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in the
A Note on the Asymptotic Number of Latin Rectangles
โ Scribed by I. Skau
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 75 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
โฆ Synopsis
The enumeration problem of Latin rectangles is formulated in terms of permanents, and two 'hard' inequalities of permanents are applied in a squeezing manner, both giving and suggesting asymptotic formulas.
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We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is found by algebraic manipulation of the operator, and the upper b
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