# Definition:Combinatorics

## Definition

**Combinatorics** is that branch of mathematics concerned with counting things.

**Combinatorial** problems are so named because they are exercises in counting the number of combinations of various objects.

It has been stated that it is the core of the discipline of discrete mathematics.

## Also known as

The field of **combinatorics** is also known as **combinatorial analysis**.

## Also see

- Results about
**combinatorics**can be found**here**.

## Historical Note

The earliest record of a problem in combinatorics was Plutarch's account of the attempt of Xenocrates of Chalcedon to find the total number of syllables that could be made from the letters of the alphabet.

According to Plutarch, Xenocrates' result was $1,002,000,000,000$ (a *myriad-and-twenty times a myriad-myriad*).

In modern times, the field of combinatorics was instigated by the investigations of the Chevalier de Méré, along with the analytical work of Blaise Pascal.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{V}$: "Greatness and Misery of Man" - 1964: A.M. Yaglom and I.M. Yaglom:
*Challenging Mathematical Problems With Elementary Solutions: Volume $\text { I }$*... (next): Problems - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**combinatorics** - 2006: Martin Gardner:
*The Colossal Book of Short Puzzles and Problems*... (previous) ... (next): Chapter $1$: Combinatorics - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**combinatorics**