Gale-Robinson Quivers and Principal Coefficients
Combinatorics
2026-02-24 v1
Abstract
In this paper, we provide a combinatorial interpretation for Laurent polynomials obtained by iteratively mutating a certain periodic quiver that has been framed with frozen vertices. This yields a family of cluster variables with principal coefficients associated to a family of integer sequences known as Gale-Robinson sequences. The work of this paper completes arguments for preliminary results announced in earlier work of Jeong-Musiker-Zhang, and relates to works of Bousquet-M\'elou-Propp-West, Speyer, Vichitkunakorn, and of Eager-Franco.
Cite
@article{arxiv.2602.19402,
title = {Gale-Robinson Quivers and Principal Coefficients},
author = {Qiyue Chen and Gregg Musiker},
journal= {arXiv preprint arXiv:2602.19402},
year = {2026}
}
Comments
40 pages, 24 figures. Comments welcome