## 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.

Algebraic
Combinatorics Seminar home