Binomial Coefficient

Jun 28, 2023

https://kconrad.math.uconn.edu/blurbs/proofs/binomcoeffintegral.pdf

写作 $\dbinom{n}{k}$，定义为 ${\displaystyle (1+x)^{n}}$的多项式展开式中，${\displaystyle x^{k}}$ 项的系数，因此一定是非负整数。 (n > k)
定义：$$\dbinom{n}{k} = \frac{n!} {(n-k)! \times k!}$$
理解：从 n 个里面选，k 个为一组，剩下为一组，内部排列

• Definition:
  • α → β is a trivial functional dependency (i.e., β ⊆ α).
  • α is a superkey for schema R.

• (α ∪ β)
• (R − (β − α))
• In the case of in dep above, α = dept name, β = {building, budget}, and in_dep is replaced by
  • (α ∪ β) = (dept name, building,budget)
  • (R − (β − α)) = (ID, name, dept name, salary)