The Laurent phenomenon

Preprint

25 April 2001

preprint
Published by arXiv in arXiv

https://doi.org/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.

Keywords

LAURENT POLYNOMIALS
LAURENT PHENOMENON
POLYNOMIALS NEED
BIRATIONAL MAPS
RECURRENCES
INTEGRALITY
CONJECTURE
PROPERTY

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Version 1, 2001-04-25, ArXiv

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