We give elementary proofs of the main theorems about the (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, the presentation, and a recent theorem of Fulton and Woodward about the minimal q -power which appears in a product of two Schubert classes.
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Anders Skovsted Buch (2003) studied this question.
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