English

The Cube Recurrence

Combinatorics 2007-05-23 v1

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 Z3\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.

Keywords

Cite

@article{arxiv.math/0403417,
  title  = {The Cube Recurrence},
  author = {Gabriel D. Carroll and David E Speyer},
  journal= {arXiv preprint arXiv:math/0403417},
  year   = {2007}
}