Odd values of the partition function
โ Scribed by Ken Ono
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 227 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In the setting of ZF, i.e., Zermelo-Fraenkel set theory without the Axiom of Choice (AC), we study partitions of Russell-sets into sets each with exactly n elements (called n-ary partitions), for some integer n. We show that if n is odd, then a Russell-set X has an n-ary partition if and only if |X|
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 n 0 , then |D(x)| log x