Schiffler's formula for A_n cluster variables and some generalizations

Hugh Thomas (U. New Brunswick)

Abstract: We will present Schiffler's formula for expanding a cluster variable as a sum of Laurent monomials in the seed variables in the A_n case (as presented in math.RT/0611956). We will discuss a generalization in the context of Fomin-Shapiro-Thurston cluster algebras associated to surfaces, and a related result in which, for an acyclic seed, we give a formula to expand a cluster variables as a sum of standard monomials in the lower cluster algebra. The new results we will be discussing are joint with Ralf Schiffler.

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