Definition:Binomial Coefficient/Notation

Definition

The notation $\dbinom n k$ for the binomial coefficient was introduced by Andreas Freiherr von Ettingshausen in his $1826$ work Die kombinatorische Analysis, als Vorbereitungslehre zum Studium der theoretischen höheren Mathematik.

It appears to have become the de facto standard in recent years.

As a result, $\dbinom n k$ is frequently voiced the binomial coefficient $n$ over $k$.

Other notations include:

$\map C {n, k}$

${}^n C_k$

${}_n C_k$

$C^n_k$

${C_n}^k$

all of which can cause a certain degree of confusion.

Sources

• 1964: A.M. Yaglom and I.M. Yaglom: Challenging Mathematical Problems With Elementary Solutions: Volume $\text { I }$ ... (previous) ... (next): Problems
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients