On the properties of the exchange graph of a cluster algebra
Combinatorics
2016-05-19 v2 Symplectic Geometry
Abstract
We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra in two cases: when is of geometric type and when is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of . Both conjectures were formulated recently by Fomin and Zelevinsky.
Keywords
Cite
@article{arxiv.math/0703151,
title = {On the properties of the exchange graph of a cluster algebra},
author = {Michael Gekhtman and Michael Shapiro and Alek Vainshtein},
journal= {arXiv preprint arXiv:math/0703151},
year = {2016}
}
Comments
Former Conjecture 2 split into Conjectures 2 and 3. Former Theorem 3 split into Theorems 4 and 5 accordingly. Former Section 2 split into Sections 2 and 3 accordingly. An error in the proof of case (i) of the former Theorem 3 (now Theorem 4) corrected, see 10 lines after equation (12)