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Results tagged with binomial-coefficients
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user 9044
For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
3
votes
2
answers
248
views
A sum related to the Johnson association scheme
Hi everyone,
In the process of studying a problem in the Johnson association scheme I came across the following sum:
$$\sum_{k\geq 0}(-1)^k\binom{n}{k}\binom{a-k}{a-b}\binom{c+k}{b}.$$
All the variab …
- 618
3
votes
1
answer
659
views
(Asymptotics of) Sum involving alternating sign Chu-Vandermonde
While considering eigenvalues of a certain Cayley graph, I came across the following sum:
$$\sum_{r=0}^{d}\sum_{i=0}^{r} (-1)^{i} \binom{w}{i}\binom{n-w}{r-i}$$
where $d$, $w$, and $n$, are all positi …
- 618