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Identities relating the number of partitions into an even and odd number of parts

✍ Scribed by Dean R Hickerson


Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
94 KB
Volume
15
Category
Article
ISSN
0097-3165

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πŸ“œ SIMILAR VOLUMES


The 2-Adic Behavior of the Number of Par
✍ Ken Ono; David Penniston πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 171 KB

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)

Decomposing complete equipartite graphs
✍ Benjamin R. Smith πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 155 KB

## 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

On the Number of Even and Odd Latin Squa
✍ Arthur A Drisko πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 358 KB

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

The multi-color Ramsey number of an odd
✍ Yusheng Li πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 73 KB

## Abstract Let __r__~__k__~(__G__) be the __k__‐color 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