Linear and Multilinear Aspects of Isomorph Rejection

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Abstract
This paper considers certain linear and multilinear aspects of the classical isomorph rejection problem. Specifically, elements of a finite set S are considered as elements of a finite dimensional vector space. Some classical and more recent formulations of Bumside's Lemma are stated and proved in this linear algebraic setting. It is observed that the specialization of S as a finite function space yields a multilinear structure on the underlying vector space. It is remarked that the multilinear structure may be exploited to achieve Pó1ya-like counting theorems

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