Identities relating the number of partitions into an even and odd number of parts
β Scribed by Dean R Hickerson
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 94 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let Q(n) denote the number of partitions of an integer n into distinct parts. For positive integers j, the first author and B. Gordon proved that Q(n) is a multiple of 2 j for every non-negative integer n outside a set with density zero. Here we show that if i 0 (mod 2 j ), then In particular, Q(n)
## Abstract In this article, we introduce a new technique for obtaining cycle decompositions of complete equipartite graphs from cycle decompositions of related multigraphs. We use this technique to prove that if __n__, __m__ and Ξ» are positive integers with __n__ β₯ 3, Ξ»β₯ 3 and __n__ and Ξ» both odd
It is shown that given an odd prime p, the number of even latin squares of order p+1 is not equal to the number of odd latin squares of order p+1. This result is a special case of a conjecture of Alon and Tarsi and has implications for various other combinatorial problems, including conjectures of R
## Abstract Let __r__~__k__~(__G__) be the __k__βcolor Ramsey number of a graph __G__. It is shown that $r\_{k}(C\_{5})\le \sqrt{18^{k}\,k!}$ for __k__β©Ύ2 and that __r__~__k__~(__C__~2__m__+ 1~)β©½(__c__^__k__^__k__!)^1/__m__^ if the Ramsey graphs of __r__~__k__~(__C__~2__m__+ 1~) are not far away fr