The Laurent phenomenon

2001/04/25 by Sergey Fomin, Andrei Zelevinsky, Fomin, Sergey +1 · 11 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.math/0104241

Abstract

A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of applications. In particular, we settle in the affirmative a conjecture of D.Gale and R.Robinson on integrality of generalized Somos sequences, and prove the Laurent property for several multidimensional recurrences, confirming conjectures by J.Propp, N.Elkies, and M.Kleber.

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