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The Permanent Rank of a Matrix

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Abstract

Define the perrank of a matrixAto be the size of the largest square submatrix ofAwith nonzero permanent. Motivated in part by the Alon–Jaeger–Tarsi Conjecture [3], we prove several results on perranks..

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Communicated by Noga, Alon

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This is part of the author's Ph.D. thesis, written under the guidance of Professor Jeff Kahn and supported by DIMACS. DIMACS is an NSF Science and Technology Center, funded under Contract STC 91-19999. E-mail: [email protected].