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The Cube Recurrence

Gabriel D. Carroll·David E Speyer
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Abstract

We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in $\mathbb{Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs.

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Gabriel D. Carroll, David E Speyer. 2004-03-24. The Cube Recurrence. https://arxiv.org/abs/math/0403417

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