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Multipartition : ウィキペディア英語版 | Multipartition 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. ==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.
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