Ramsey problems in additive number theory
نویسندگان
چکیده
منابع مشابه
Some Problems in Additive Number Theory
(3) f(x) = (log x/log 2) + 0(1)? 1\Mloser and I asked : Is it true that f(2 11) >_ k+2 for sufficiently large k? Conway and Guy showed that the answer is affirmative (unpublished) . P. Erdös, Problems and results in additive number theory, Colloque, Théorie des Nombres, Bruxelles 1955, p . 137 . 2. Let 1 < a 1< . . . < ak <_ x be a sequence of integers so that all the sums ai,+ . . .+ais, i 1 <...
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In a note in this Journal [16 (1941), 212-215], Turan and I proved, among other results, the following : Let a l < a2 < . . . < a, < n be a sequence of positive integers such that the sums aj+a; are all different . Then x < n'1 +0(n1 ) . On the other hand, there exist such sequences with x >n1(2---e), for any e >0 . Recently I noticed that J . Singer, in his paper "A theorem in finite projectiv...
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1. Infroduction. Let A be a sequence of positive integers. Define P(A) to be the set of all integers representable as a sum of distinct terms of A. Note that if A contains a repeated value, we are free to use it as many times as it occurs in A. We call A complete if every sufficiently large positive integer is in P(A), and entirely complete if every positive integer is in P(A). Completeness pro...
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We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every twocoloring of the edges of the complete graph KN contains a monochromatic copy of H. A famous resul...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1993
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-64-4-341-355