A Periodicity Theorem for the Octahedron Recurrence
Combinatorics
2007-05-23 v2
Abstract
We investigate a variant of the octahedron recurrence which lives in a 3-dimensional lattice contained in [0,n] x [0,m] x R. Generalizing results of David Speyer math.CO/0402452, we give an explicit non-recursive formula for the values of this recurrence in terms of perfect matchings. We then use it to prove that the octahedron recurrence is periodic of period n+m. This result is reminiscent of Fomin and Zelevinsky's theorem about the periodicity of Y-systems.
Cite
@article{arxiv.math/0604289,
title = {A Periodicity Theorem for the Octahedron Recurrence},
author = {Andre Henriques},
journal= {arXiv preprint arXiv:math/0604289},
year = {2007}
}
Comments
22 pages, (a few pictures added, section 3 has been reorganized)