A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
Rings and Algebras
2015-06-29 v2 Combinatorics
Abstract
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra.
Cite
@article{arxiv.1409.8177,
title = {A Combinatorial Formula for Certain Elements of Upper Cluster Algebras},
author = {Kyungyong Lee and Li Li and Matthew R. Mills},
journal= {arXiv preprint arXiv:1409.8177},
year = {2015}
}