2006/04/12 by André Henriques, Henriques, Andre
Mathematics · Physics and Astronomy · #05A99 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.math/0604289
openalex publication_date 2006/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.