# The Cube Recurrence

@article{Carroll2004TheCR, title={The Cube Recurrence}, author={Gabriel D. Carroll and David E Speyer}, journal={Electron. J. Comb.}, year={2004}, volume={11} }

We construct a combinatorial model that is described by the cube recurrence, a quadratic recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in ${\Bbb Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky about the structure of these polynomials, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences, including the Somos-6 and Somos-7 sequences. We also indicate how the model… Expand

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