In number theory and combinatorics, a multipartition of a positive integer n is a way of writing n as a sum, each element of which is in turn a partition. The concept is also found in the theory of Lie algebras.
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 ai and the ai sum to n. The number of r-component multipartitions of n is denoted Pr(n). Congruences for the function Pr(n) have been studied by A. O. L. Atkin.
- George E. Andrews (2008). "A survey of multipartitions". In Alladi, Krishnaswami. Surveys in Number Theory. Developments in Mathematics. 17. Springer-Verlag. pp. 1–19. ISBN 978-0-387-78509-7. Zbl 1183.11063.
- Fayers, Matthew (2006). "Weights of multipartitions and representations of Ariki–Koike algebras". Advances in Mathematics. 206 (1): 112–144. Zbl 1111.20009. doi:10.1016/j.aim.2005.07.017.
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