Lotteries and truncated binomial coefficients
✍ Scribed by Zoltán Sasvári; Michael Kücken
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 107 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We consider the expression
and investigate for which k and n is P(k, n) an integer. We find integer solutions k and m of the equation P(k, n) = m for a given integer m and approximate real solutions x = x(k) of the equation P(k, x) = 2. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
📜 SIMILAR VOLUMES
In this paper, we present a method for obtaining a wide class of combinatorial identities. We give several examples; some of them have already been considered previously, and others are new. 2002 Elsevier Science (USA)
Using binomial coefficients the Clebsch-Gordan and Gaunt coefficients were calculated for extremely large quantum numbers. The main advantage of this approach is directly calculating these coefficients, instead of using recursion relations. Accuracy of the results is quite high for quantum numbers \
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.