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We prove a general identity for a 3F2 hypergeometric function over a finite field Fq, 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 3F2 as the square of a 2F1. As another application, we evaluate an infinite(More)
Recombineering has been an essential tool for genetic engineering in microbes for many years and has enabled faster, more efficient engineering than previous techniques. There have been numerous studies that focus on improving recombineering efficiency, which can be divided into three main areas: (i) optimizing the oligo used for recombineering to enhance(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)
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)
An episode of the television series Futurama features a two-body mind-switching machine, which will not work more than once on the same pair of bodies. After the Futurama community engages in a mind-switching spree, the question is asked, “Can the switching be undone so as to restore all minds to their original bodies?” Ken Keeler found an algorithm that(More)
A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p > 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his(More)