# Partitions

• Tom M. Apostol
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Until now this book has been concerned primarily with multiplicative number theory, a study of arithmetical functions related to prime factorization of integers. We turn now to another branch of number theory called additive number theory. A basic problem here is that of expressing a given positive integer n as a sum of integers from some given set A, say
$$A = \left\{ {{a_1},{a_2},...} \right\}$$
, where the elements a i are special numbers such as primes, squares, cubes, triangular numbers, etc. Each representation of n as a sum of elements of A is called a partition of n and we are interested in the arithmetical function A(n) which counts the number of partitions of i into summands taken from A. We illustrate with some famous examples.

## Keywords

Partition Function Recursion Formula Arithmetical Function Combinatorial Proof Partition Identity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.