Regular perfect systems of differences sets

✍ Scribed by Anton Kotzig; Jean Turgeon

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 424 KB
• Volume: 20
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(77)90064-4

✦ Synopsis

_xk, 113 6 k <j s I,) be thcit difference sets. We shah say that the system ,S = (S, S2,. . ,, S,) is perfect if Each D' is called a component of the system. A perfect system of difference sets is caifed regular if rl = r2 = ---= r, = r. We shall then speak of a perfect (I, s)-system.

In this paper, wz present a partial answer to the following question: for which uulwes of r and s do perfect (r, s)-sy.stems exist ? The authors want to take this opportunity to express their gratitude to Professor Paul Erdiis, whr, first formulated this problem to them during a friendly discussion.

We shah use the notation

In particular, we shah write d, ' = d& for the "maximal difference" ti each component;