Séminaire Lotharingien de Combinatoire, 78B.40 (2017), 12 pp.
Dimers, Crystals and Quantum Kostka Numbers
We relate the counting of honeycomb dimer configurations on the
cylinder to the counting of certain vertices in Kirillov-Reshetikhin
crystal graphs. We show that these dimer configurations yield the
quantum Kostka numbers of the small quantum cohomology ring of the
Grassmannian, i.e., the expansion coefficients when multiplying a
Schubert class repeatedly with different Chern classes. This allows
one to derive sum rules for Gromov-Witten invariants in terms of dimer
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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