The Octahedron Recurrence and Rsk-correspondence
نویسنده
چکیده
Wemake the statement rigorous that the Robinson–Schensted–Knuth correspondence is a tropicalization of the Dodgson condensation rule.
منابع مشابه
Oscillating tableaux and a superanalogue of the Robinson-Schensted-Knuth correspondence
In this paper, we investigate the super RSK correspondence, first introduced by Pak and Postnikov (1994), which generalizes both the RSK correspondence and the dual RSK correspondence. The bijection relates objects that are known as oscillating supertableau and (intransitive) supergraphs. We prove a number of theorems that were stated in the original paper of Pak and Postnikov, but whose proofs...
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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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By the geometric Satake correspondence, the number of components of certain fibres of the affine Grassmannian convolution morphism equals the tensor product multiplicity for representations of the Langlands dual group. On the other hand, in the case of GLn, combinatorial objects called hives also count tensor product multiplicities. The purpose of this paper is to give a simple bijection betwee...
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We prove that the Robinson-Schensted-Knuth correspondence is a gl∞-crystal isomorphism between two realizations of the crystal graph of a generalized Verma module with respect to a maximal parabolic subalgebra of gl∞. A flagged version of the RSK correspondence is derived in a natural way by computing a Demazure crystal graph of a generalized Verma module. As an application, we discuss a relati...
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تاریخ انتشار 2007