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.<ref name="Andrews2008">{{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: congruences and identities | pages=1–19 | zbl=1183.11063}}</ref> The concept is also found in the theory of Lie algebras.<ref name="Andrews2008"/><ref>{{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 }}</ref>
==r-component multipartitions== An ''r''-component multipartition of an integer ''n'' is an ''r''-tuple of partitions ''λ''<sup>(1)</sup>, ..., ''λ''<sup>(r)</sup> where each ''λ''<sup>(''i'')</sup> is a partition of some ''a''<sub>''i''</sub> and the ''a''<sub>''i''</sub> sum to ''n''. The number of ''r''-component multipartitions of ''n'' is denoted ''P''<sub>''r''</sub>(''n''). Congruences for the function ''P''<sub>''r''</sub>(''n'') have been studied by A. O. L. Atkin.<ref name="Andrews2008"/><ref>{{cite journal | last1=Atkin | first1=A. O. L. | authorlink1=A. O. L. Atkin | title=Ramanujan congruences for <math>p_{-k}(n)</math> | journal=Canadian Journal of Mathematics | volume=20 | date=1968 | pages=67-78 | doi=10.4153/CJM-1968-009-6 | doi-access=free}}</ref>
==References==
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Category:Number theory Category:Combinatorics
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