article · 1998
Thin Complete Subsequence
Norbert Hegyvári
Cited by 0Abstract and details only
Abstract
A is said to be complete if every suÆciently large integer belongs to sumset of A. A 0 is thin comlete subsequence of A if A 0 is complete and A 0 (x) = (1 + o(1)) log 2 x. It is proved that lim n!1 a n+1 =a n = 1 implies the existence of thin complete subsequence. 1. Introduction The well known theorem of Lagrange states that every nonnegative integer n is the sum of four squares. In other words the sequence S = f1; 4; : : : ; n 2 ; : : :g is bases of order four. Generally if A is a bases of order h then A(x) x 1=h , where A(x) is the counting function of A. Wirsing dened the notion of thin bases; A is thin bases of order h if A(x) < c 0 x 1=h ; (c 0 > 0). By a non-constructive method Wirsing proved [1] that S has a subbases S 0 which is almost thin, proving S 0 (x) = O(x 1=4 (log x) 1=4 ). Later J. Spencer [2] gave a short proof for it, using an important tool of probabilistic method, the Janson's inequality. We merely mention it is not even known an ...
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Hegyvári, N. (1998). Thin Complete Subsequence.
Hegyvári, Norbert. “Thin Complete Subsequence.” 1998.
Hegyvári, Norbert. 1998. “Thin Complete Subsequence.”
Hegyvári, N. (1998) ‘Thin Complete Subsequence’.
@article{hegyvari1998thin,
title = {{Thin Complete Subsequence}},
author = {Hegyvári, Norbert},
year = {1998}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.