On the complexity of the permanent in various computational models
Abstract
We answer a question in [Landsberg, Ressayre, 2015], showing the regular determinantal complexity of the determinant detm is O(m3). We answer questions in, and generalize results of [Aravind, Joglekar, 2015], showing there is no rank one determinantal expression for permm or detm when m >= 3. Finally we state and prove several "folklore" results relating different models of computation.
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