Dimers, crystals and quantum Kostka numbers
arXiv:1702.07162
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.
12 pages,4 figures, extended abstract for FPSAC 2017, London (accepted)