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 ZP\mathbf{Z}\mathbf{P} where P\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.

Created on January 11, 2012 at 18:36:42. See the history of this page for a list of all contributions to it.