A Periodicity Theorem for the Octahedron Recurrence
Andre Henriques
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.
Create a lesson
Related papers
Graded Ehrhart theory for hypersimplices
Nathaniel Libman, Weston Miller
Closing the gap and settling the problem of queens on an n× n board, each attacking at most one other
Kristina Ago, Bojan Bašić, Radojka Ciganović
Leading term strandings for webs
Michael Bo, Madelyn Burns, Junyang Chen et al.
Refutation of the Non-Cancelling-Intersections Conjecture
Hermann Wilhelm
Asymptotic Bounds for Online Ramsey Numbers of Stars versus Long Paths and Cycles
Sam Beilis, Israel R. Curbelo, Elizabeth R. Koizumi
The Erdos--Gallai bound for consecutive even cycle lengths
Yaobin Chen, Hong Liu, Xia Wang et al.