Regular perfect systems of differences sets
نویسندگان
چکیده
منابع مشابه
Irregular Extremal Perfect Systems of Difference Sets
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 general problem raised by the work of Kreweras and Loeb concerns the existence of partitions of runs of consecutive integers into sets, known as sets of iterated differences, the s(s + 1 )/2 elements of which can be expressed as certain linear combinations of s integer valued parameters. In this paper we study the case of four parameters. By examining properties already present in examples wi...
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For s ≥ 2, a set {a(i, j) : 1 ≤ j ≤ s + 1 − i ≤ s} where a(1, j), 1 ≤ j ≤ s, are some prescribed integers and a(i + 1, j) = |a(i, j) − a(i, j + 1)|, for 1 ≤ i < s and 1 ≤ j ≤ s − i , 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. Kreweras and Loeb suggested the problem of partitioning a run of ms(s+1)/2 integers starting w...
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A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2, . . . expresses a non-negative integer n as a sum n = ∑i j=0 ajuj . In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1, . . .) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1977
ISSN: 0012-365X
DOI: 10.1016/0012-365x(77)90064-4