Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651404 | Discrete Mathematics | 2006 | 9 Pages |
Abstract
A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A d-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or d times. In this paper we give a construction for minimal d-homogeneous latin trades of size dm , for every integer d⩾3d⩾3, and m⩾1.75d2+3m⩾1.75d2+3. We also improve this bound for small values of d. Our proof relies on the construction of cyclic sequences whose adjacent sums are distinct.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Nicholas J. Cavenagh, Diane M. Donovan, Emine Şule Yazıcı,