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Degree bounds in quantum Schubert calculus. (English) Zbl 1064.14066
The aim of the paper under review is to give a new proof of a recent result of [W. Fulton and C. Woodward [J. Algebr. Geom. 13, 641–661 (2004; Zbl 1081.14076)] related to the smallest degree that appears in the expansion of the product of two Schubert cycles in the small quantum cohomology ring of a Grassmann variety. The author’s approach is combinatorial, and this method also yields an alternative characterization of this smallest degree in terms of the rim hook formula for the quantum product.

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14M15 Grassmannians, Schubert varieties, flag manifolds
05E05 Symmetric functions and generalizations
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