Investigations regarding Partitions and Multipartitions
نویسنده
چکیده
We consider several topics in the theory of partitions, focusing on questions regarding multipartitions. Results include the formulation of a combinatorial explanation of the crank statistic generalized to multipartitions; the conjecture and proof of several multipartition identities; the calculation of the number of k-partitions of n with crank n, n-1, or n-2; the construction of a crank-reversing bijection on the partitions of n; the definition, and characterization of movable multipartitions, the proof of several partition identities for movable multipartitions; the definition of friendly partitions, and a generating function for the number of friendly partitions of n.
منابع مشابه
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We give a proof of a conjecture that Kleshchev multipartitions are those partitions which parametrize non-zero simple modules obtained as factor modules of Specht modules by their own radicals.
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