On the additive completion of linear recurrence sequences
On the additive completion of linear recurrence sequences
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DOI：
10.1007/bf02019434
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发表时间：
1978-12
影响因子：
0.8
通讯作者：
I. Ruzsa
中科院分区：
文献类型：
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作者：
I. Ruzsa
(1.1) B (x) > max y-k al ~ y < x (y), 1 < 2 <…另一方面，LORENTZ[3]证明了，对于每一个非空集合A，存在一个满足~ 1-~ log A (y)(1.2) B (x)< c, y= A, A (y)且具有绝对常数c的互补集合B（在分子中插入项1只是为了避免在A={al}的情况下出现错误结果）。这些界限之间有相当大的差距。例如，如果A具有正的低密度，则（1.1）和式（1.2）只给出
(1.1) B (x)> max y-k, al~ y< x A (y) where a 1< a 2<... are the elements of A. On the other hand, LORENTZ [3~ proved~ hat for every non-empty set A there exists a complementary set B satisfying~ 1-~ log A (y)(1.2) B (x)< c, y= a, A (y) with an absolute constant c.(The term 1 is inserted into the numerator only to avoid the wrong result in case A={al}.) There is a considerable gap between these bounds. For example, if A has positive lower density, then (1.1) and (1.2) give only