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Uniform perfect systems of sets of iterated differences of size 41

โœ Scribed by G.M. Hamilton; C. Ramsay; I.T. Roberts; D.G. Rogers

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
724 KB
Volume
162
Category
Article
ISSN
0012-365X

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๐Ÿ“œ SIMILAR VOLUMES

Regular Perfect Systems of Sets of Itera
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โœ G.M. Hamilton; I.T. Roberts; D.G. Rogers ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 192 KB

For s โ‰ฅ 2, a set {a(i, j) : 1 โ‰ค j โ‰ค s + 1i โ‰ค s} where a(1, j), 1 โ‰ค j โ‰ค s, are some prescribed integers and a(i + 1, j) = |a(i, j)a(i, j + 1)|, for 1 โ‰ค i < s and 1 โ‰ค j โ‰ค si, is called a set of iterated differences. Such a set has size s and is full if it contains s(s + 1)/2 distinct integers. Krewera

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\_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 pape

On critical perfect systems of differenc
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โœ D.G. Rogers ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 773 KB

A perfect system of difference sets with threshold c is a partition of a consecutive run of integers beginning with c into full difference sets of valency at least 2. The BKT inequality, due to Bermond, Kotzig and Turgeon gives a necessary condition for the existence of such systems; systems for whi