Asymptotic complements in the integers
نویسندگان
چکیده
منابع مشابه
On the Asymptotic Density of Sets of Integers. Ii
where a,, and b, equal 0 or 1, the set A (resp. B) appearing as the set of those n such that a,, = 1 (resp. b, = 1). It seems a rather difficult problem to describe explicitly the structure of all such direct factors, although the theorem demonstrated in [5] and our present Theorem 1 shed some light on the situation by proving the existence of their asymptotic densities. (The corresponding addi...
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Let Ak = {0 = a1 < a2 < ... < ak} and B = {0 = b1 < b2 < ... < bn ...} be sets of k integers and infinitely many integers, respectively. Suppose B has asymptotic density x t d(B) x. If, for every integer n _> 0, there is at most one representation n a^ + bj , then we say that Ak has a packing complement of density j> x. Given Ak and x9 there is no known algorithm for determining whether or not ...
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and the rows and columns are arranged in decreasing order: ωi,j ≥ ωi+1,j, ωi,j ≥ ωi,j+1 for all i, j ≥ 1. The non-zero entries ωi,j > 0 are called parts of ω. Sometimes, for the sake of brevity, the zeroes in the array (1) are deleted. For instance, the abbreviation 3 2 1 1 1 is assumed to present a plane partition of n = 8 having 2 rows and 5 parts. It seems that MacMahon was the first who int...
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In this paper, we prove the following result: Let A be an infinite set of positive integers. For all positive integer n, let τn denote the smallest element of A which doesn’t divide n. Then we have lim N→+∞ 1 N N ∑
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2020
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.11.015