The Laurent phenomenon. (English) Zbl 1012.05012

Summary: 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.


05A15 Exact enumeration problems, generating functions
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