A periodicity theorem for the octahedron recurrence
نویسنده
چکیده
The octahedron recurrence lives on a 3-dimensional lattice and is given by f (x, y, t + 1) = ( f (x + 1, y, t) f (x − 1, y, t) + f (x, y + 1, t) f (x, y − 1, t))/ f (x, y, t − 1). In this paper, we investigate a variant of this recurrence which lives in a lattice contained in [0, m] × [0, n] × R. Following Speyer, we give an explicit non-recursive formula for the values of this recurrence and use it to prove that it is periodic of period n + m. We then proceed to show various other hidden symmetries satisfied by this bounded octahedron recurrence.
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تاریخ انتشار 2007