| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4595494 | Journal of Number Theory | 2007 | 7 Pages |
Abstract
Let N be the set of all positive integers and D a subset of N. Let p(D,n) be the number of partitions of n with parts in D and let |D(x)| denote the number of elements of D not exceeding x. It is proved that if D is an infinite subset of N such that p(D,n) is even for all n⩾n0, then |D(x)|⩾logx/log2−logn0/log2. Moreover, if D is an infinite subset of N such that p(D,n) is odd for all n⩾n0 and , then |D(x)|⩾logx/log2−logn0/log2. These lower bounds are essentially the best possible.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
