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Multipartition
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<h2 id="r-component-multipartitions">r-component multipartitions</h2> <p>An <i>r</i>-component multipartition of an integer <i>n</i> is an <i>r</i>-tuple of partitions <i>λ</i>(1), ..., <i>λ</i>(r) where each <i>λ</i>(<i>i</i>) is a partition of some <i>a</i><i>i</i> and the <i>a</i><i>i</i> sum to <i>n</i>. The number of <i>r</i>-component multipartitions of <i>n</i> is denoted <i>P</i><i>r</i>(<i>n</i>). Congruences for the function <i>P</i><i>r</i>(<i>n</i>) have been studied by <a href="/facts/A._O._L._Atkin/3SsYWcb1">A. O. L. Atkin</a>. </p> <ul><li><a href="/facts/George_Andrews_(mathematician)/x58GmSuR">George E. Andrews</a> (2008). "A survey of multipartitions". In <a href="/facts/Krishnaswami_Alladi/pgLb1aN7">Alladi, Krishnaswami</a> (ed.). <i>Surveys in Number Theory</i>. Developments in Mathematics. Vol. 17. <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. pp. 1–19. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-78509-7. <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:1183.11063">1183.11063</a>.</li> <li>Fayers, Matthew (2006). <a href="https://doi.org/10.1016%2Fj.aim.2005.07.017">"Weights of multipartitions and representations of Ariki–Koike algebras"</a>. <i><a href="/facts/Advances_in_Mathematics/kXtcl4pM">Advances in Mathematics</a></i>. 206 (1): 112–144. <a href="/facts/CiteSeerX_(identifier)/SceDmd3c">CiteSeerX</a> <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.538.4302">10.1.1.538.4302</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.aim.2005.07.017">10.1016/j.aim.2005.07.017</a>. <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:1111.20009">1111.20009</a>.</li></ul>