Arrays and the Octahedron Recurrence
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چکیده
منابع مشابه
A periodicity theorem for the octahedron recurrence
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 u...
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We show that a family of multivariate polynomials recently introduced by Bessenrodt and Stanley can be expressed as solution of the octahedron recurrence with suitable initial data. This leads to generalizations and explicit expressions as path or dimer partition functions.
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The A∞ T-system, also called the octahedron recurrence, is a dynamical recurrence relation. It can be realized as mutation in a coefficient-free cluster algebra (Kedem 2008, Di Francesco and Kedem 2009). We define T-systems with principal coefficients from cluster algebra aspect, and give combinatorial solutions with respect to any valid initial condition in terms of partition functions of perf...
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We introduce a recurrence which we term the multidimensional cube recurrence, generalizing the octahedron recurrence studied by Propp, Fomin and Zelevinsky, Speyer, and Fock and Goncharov and the three-dimensional cube recurrence studied by Fomin and Zelevinsky, and Carroll and Speyer. The states of this recurrence are indexed by tilings of a polygon with rhombi, and the variables in the recurr...
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Wemake the statement rigorous that the Robinson–Schensted–Knuth correspondence is a tropicalization of the Dodgson condensation rule.
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تاریخ انتشار 2005