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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