On critical perfect systems of difference sets
نویسندگان
چکیده
منابع مشابه
Further results on irregular, critical perfect systems of difference sets I: split systems
Hamilton, G.M. and D.G. Rogers, Further results on irregular, critical perfect systems of difference sets I: split systems, Discrete Mathematics 102 (1992) 25-45. An (m, n; U, v; c)-system is a collection of components, m of valency u 1 and n of valency v 1, whose difference sets form a perfect system with threshold c. If there is an (m, n; 3, 6; c)-system, then m 22~ 1; and if there is a (2c 1...
متن کاملFurther results on irregular, critical perfect systems of difference sets II: systems without splits
Hayasaka, T., S. Saito and D.G. Rogers, Further results on irregular, critical perfect systems of difference sets II: systems without splits, Discrete Mathematics 110 (1992) 135-154. An (m, n; u, v; c)-system is a collection of components, m of valency u 1 and n of valency u 1, whose difference sets form a perfect system with threshold c. If there is an (m, n; 3, 6; c)-system, then m 22~ 1; and...
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An {m, n;u, u;c)-system is a perfect system of difference sets with m components of size u— 1 and n components of size v— 1 having threshold c. A necessary condition for the existence of an (m, n; u, 6; c)system for u = 3 or 4 is that m ^ 2c— 1. We show that, in the extremal case when m = 2c— 1, there are (2c— 1, n; 3, 6; c)-systems for c ^ 3 when n = 1, and for c ^ 5 when n = 2, with a few pos...
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A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...
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We give some improvements on the BKT inequality, an inequality for perfect systems of difference sets due to Bermond, Kotzig, and Turgeon, and consider, in particular, their implications for the critical case in which the BKT inequality holds with equality.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0103-b