Cluster expansion formulas and perfect matchings

Details Cluster expansion formulas and perfect matchings Cluster expansion formulas and perfect matchings

2008-10-20

arxiv.org/abs/0810.3638v1

Mathematics

Representation Theory

19 pages, 8 figures

Scientific paper

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph $G_{T,\gamma}$ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula for these Laurent polynomial expansions in terms of subgraphs of the graph $G_{T,\gamma}$.

Affiliated with

Also associated with

No associations

Rating

Cluster expansion formulas and perfect matchings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cluster expansion formulas and perfect matchings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cluster expansion formulas and perfect matchings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-266499