IP sets, Hilbert cubes
Copyright policy )IP sets, Hilbert cubes
Summary: Given a subset \(E\) of the set of natural numbers, \(FS(E)\) is defined as the collection of all sums of elements of finite subsets of \(E\) and any translation of \(FS(E)\) is said to be a Hilbert cube. We estimate the rate of growth of \(E\) given that \(FS(E)\) avoids a set of multiplies of a given infinite set of primes. The results are related to a result which states that there exists an infinite Hibert cube contained in the set of square-free numbers.
IP-set, Other combinatorial number theory, Ramsey theory, Relations of ergodic theory with number theory and harmonic analysis, Hilbert cube
IP-set, Other combinatorial number theory, Ramsey theory, Relations of ergodic theory with number theory and harmonic analysis, Hilbert cube
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