Geodesic
The cube recurrence
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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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 might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs.
DOI : 10.37236/1826
Classification : 05A15, 11B83
Mots-clés : Laurent polynomials, Gale-Robinson sequences, perfect matchings, bipartite planar graphs 
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     author = {Gabriel D. Carroll and David Speyer},
     title = {The cube recurrence},
     journal = {The electronic journal of combinatorics},
     year = {2004},
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     number = {1},
     doi = {10.37236/1826},
     zbl = {1060.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1826/}
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Gabriel D. Carroll; David Speyer. The cube recurrence. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1826

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