A periodicity theorem for the octahedron recurrence

@article{Henriques2006APT,
  title={A periodicity theorem for the octahedron recurrence},
  author={Andr{\'e} Henriques},
  journal={Journal of Algebraic Combinatorics},
  year={2006},
  volume={26},
  pages={1-26}
}
  • André Henriques
  • Published 2006
  • Mathematics
  • 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 $$[0,m] \times [0,n] \times \mathbb R$$. 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… CONTINUE READING

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