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Say that two Hamiltonian paths P 1 and P 2 of Gare neighbors if they have exactly n 2 edges in common; also say a Hamiltonian path P and a Hamiltonian cycle Cof Gare neighbors if every edge 6 •monolithic if f = ghfor some g,h ∈N 0[x±1] implies that either g or his a monomial of N 0[x±1], and •hyper-monolithic if fis not a monomial and either k 0 −k 1 <k i −k This page provides instructions for applying to PRIMES-USA , a nationwide research program for high school juniors and sophomores living in the U. The Research Science Institute (RSI) is considered the most prestigious summer program in STEM for high school students in the United States. See also 2022 Spring Term conference and 2022 December mini-conference. Research experience before PRIMES. You can apply to both sections at the same time, but you can be admitted only to one. MIT PRIMES (Program for Research in Mathematics, Engineering and Science) is a free, year-long after-school research program for high school students. 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