Semi-magic matrices for dihedral groups
Abstract
After reviewing the group structure and representation theory for the dihedral group D2n, we consider an intertwining operator from the group algebra C[D2n] into a corresponding space of semi-magic matrices. From this intertwining operator, one obtains the generating function for enumerating the associated semi-magic squares with fixed line sum and an algebra extending the circulant matrices. While this work complements the approach to D2n through permutation polytopes, we use only methods from representation theory.
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