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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 .


[1] J. Riordan, "An introduction to combinational analysis" , Wiley (1958)
How to Cite This Entry:
Denumerant. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.E. Tarakanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article