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Séminaire Lotharingien de Combinatoire, 78B.40 (2017), 12 pp.

# Christian Korff

# Dimers, Crystals and Quantum Kostka Numbers

**Abstract.**
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
configurations.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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