# Manuals/calci/PARTP

PARTP (n,k)

where

• and are any integers.
• PARTP() shows the number of partitions of a given number.

## Description

PARTP(n,k)

• is any integer. is the number of ways.
• A partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.
• Two sums that differ only in the order of their summands are considered the same partition.
• By convention, partitions are usually ordered from largest to smallest.
• Partition of a number is also called the number of unrestricted partition.
• When explicitly listing the partitions of a number n, the simplest form is the so-called natural representation which simply gives the sequence of numbers in the representation.
• The multiplicity representation instead gives the number of times each number occurs together with that number.

## Examples

1. PARTP(10,3) = 8
2. PARTP(54,10) = 29292

Partitions