Multipartition
{{No footnotes|date=November 2024}}
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 an integer partition. The concept is also found in the theory of Lie algebras.
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 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.
References
- {{cite book | editor1-first=Krishnaswami | editor1-last=Alladi |editor1-link= Krishnaswami Alladi | title=Surveys in Number Theory | series=Developments in Mathematics | volume=17 | publisher=Springer-Verlag | year=2008 | isbn=978-0-387-78509-7 | author=George E. Andrews | authorlink=George Andrews (mathematician) | chapter=A survey of multipartitions | pages=1–19 | zbl=1183.11063 }}
- {{cite journal | journal=Advances in Mathematics | volume=206 | issue=1 | year=2006 | pages=112–144 | title=Weights of multipartitions and representations of Ariki–Koike algebras | first=Matthew | last=Fayers | doi=10.1016/j.aim.2005.07.017 | doi-access=free | zbl=1111.20009 | citeseerx=10.1.1.538.4302 }}
{{combin-stub}}