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29 March 2024
 
  » arxiv » math/0604289

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A Periodicity Theorem for the Octahedron Recurrence
Andre Henriques ;
Date 12 Apr 2006
Subject Combinatorics
AbstractWe 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.
Source arXiv, math/0604289
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