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The problem of irregular perfect systems of sets of iterated differences

โœ Scribed by Colin Ramsay; Douglas G. Rogers

Publisher
Springer Japan
Year
1997
Tongue
English
Weight
436 KB
Volume
13
Category
Article
ISSN
0911-0119

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๐Ÿ“œ SIMILAR VOLUMES

Regular Perfect Systems of Sets of Itera
Regular Perfect Systems of Sets of Iterated Differences
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

Regular perfect systems of differences s
Regular perfect systems of differences sets
โœ Anton Kotzig; Jean Turgeon ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 424 KB

\_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
On critical perfect systems of difference sets
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