Manuals/calci/PARTP

PARTP (n,k)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} are any integers.

Description

This function shows the number of partitions of a given number.
In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle PARTP (n,k)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is any integer.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} 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.