Laurent phenomenon

While the composition of birational maps given by Laurent polynomials is in general not a Laurent polynomial there is a number of systematic situations when this is true. In particular, in a cluster algebra, any cluster variable is expressed in terms of any given cluster as a Laurent polynomial with coefficients in the integral group ring $\mathbf{Z}\mathbf{P}$ where $\mathbf{P}$ is the coefficient group. An explanation in the quantum case, from a Hodge-theoretic point of view, has recently being offered by A. Efimov.

- Sergey Fomin, Andrei Zelevinsky,
*The Laurent phenomenon*, math.CO/0104241 - Sergey Fomin, Andrei Zelevinsky,
*Cluster algebras I: Foundations*, arxiv/0104151 - Alexander I. Efimov,
*Quantum cluster variables via vanishing cycles*, arxiv/1112.3601

Created on January 11, 2012 18:36:42
by Zoran Škoda
(161.53.130.104)