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Binomial Coefficients and Zero-Sum Ramsey Numbers

✍ Scribed by Yair Caro

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 307 KB
Volume: 80
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2812

No coin nor oath required. For personal study only.

✦ Synopsis

A counting argument is developed and divisibility properties of the binomial coefficients are combined to prove, among other results, that

where K n , resp. K k n , is the complete, resp. complete k-uniform, hypergaph and R(K n , Z p ), R(K k n , Z 2 ) are the corresponding zero-sum Ramsey numbers.

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## Abstract As a consequence of our main result, a theorem of Schrijver and Seymour that determines the zero sum Ramsey numbers for the family of all __r__‐hypertrees on __m__ edges and a theorem of Bialostocki and Dierker that determines the zero sum Ramsey numbers for __r__‐hypermatchings are com