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We prove a general identity for a 3 F 2 hypergeometric function over a finite field F q , where q is a power of an odd prime. A special case of this identity was proved by Greene and Stanton in 1986. As an application, we prove a finite field analogue of Clausen's Theorem expressing a 3 F 2 as the square of a 2 F 1. As another application, we evaluate an(More)
We generalize two mind-switching problems that arise in connection with the popular sci-fi television series Futurama and Stargate SG-1. Optimal solutions to these problems are found by answering the following question about a permutation σ expressed as a product of nontrivial disjoint cycles. " When writing σ as a product of distinct transpositions none(More)
Rewiring and optimization of metabolic networks to enable the production of commercially valuable chemicals is a central goal of metabolic engineering. This prospect is challenged by the complexity of metabolic networks, lack of complete knowledge of gene function(s), and the vast combinatorial genotype space that is available for exploration and(More)
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