# Denumerant

From Encyclopedia of Mathematics

The number of partitions of an integer into parts equal to , i.e. the number of solutions in non-negative integers of the equation

The generating function of the denumerants is

The simplest method of computing a denumerant is by Euler's recurrence relation:

Explicit formulas for certain denumerants may be obtained from the following theorem: If is the least common multiple of the numbers , then the denumerant

is a polynomial of degree with respect to .

#### References

[1] | J. Riordan, "An introduction to combinational analysis" , Wiley (1958) |

**How to Cite This Entry:**

Denumerant.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Denumerant&oldid=16405

This article was adapted from an original article by V.E. Tarakanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article