number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

, a multipartition of a positive

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

''n'' is a way of writing ''n'' as a sum, each element of which is in turn a

partition Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

. The concept is also found in the theory of

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

r-component multipartitions

An ''r''-component multipartition of an integer ''n'' is an ''r''-tuple of partitions λ⁽¹⁾,...,λ^(r) where each λ^(''i'') is a partition of some ''a''_''i'' and the ''a''_''i'' sum to ''n''. The number of ''r''-component multipartitions of ''n'' is denoted ''P''_''r''(''n''). Congruences for the function ''P''_''r''(''n'') have been studied by

A. O. L. Atkin Arthur Oliver Lonsdale Atkin (31 July 1925 – 28 December 2008), who published under the name A. O. L. Atkin, was a British mathematician. As an undergraduate during World War II, Atkin worked at Bletchley Park cracking German codes. He receiv ...

References

* * Number theory Combinatorics {{combin-stub