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On the parity of broken\(k\)-diamond partitions

✍ Scribed by Chaubey, Sneha; Cheng, Wei; Malik, Amita; Zaharescu, Alexandru

Book ID: 125372753
Publisher: Springer-Verlag
Year: 2014
Tongue: German
Weight: 319 KB
Volume: 60
Category: Article
ISSN: 0430-3202
DOI: 10.1007/s11565-014-0211-6

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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