arXiv:math/0104241 Abstract

arXiv:math/0104241 [math.CO]Abstract References Reviews Resources

The Laurent phenomenon

Published 2001-04-25Version 1

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.

Comments: 21 pages

Categories: math.CO

Subjects: 14E05

Keywords: laurent phenomenon, sometimes-quite unexpectedly-it, birational maps, multidimensional recurrences, conjecture

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