โ Scribed by Christine Bessenrodt
No coin nor oath required. For personal study only.
An explicit bijection is constructed between partitions of a positive integer n with exactly j even parts which are all different, and bipartitions (x1; n2) of n into distinct parts such that 1(n2)=j and max n2 <I(aI); this implies an identity due to Lebesgue. The construction is inspired by a version of Sylvester's bijective proof of Euler's identity using the 2-modular MacMahon diagram. This vergion and its generalization easily imply a number of refinements of Euler's, respectively, Lebesgue's identity.
๐ SIMILAR VOLUMES
Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of li
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