Frieze matrices and infinite frieze patterns with coefficients

Abstract

Frieze patterns are combinatorial objects that are deeply related to cluster theory. Determinants of frieze patterns arise from triangular regions of the frieze, and they have been considered in previous works by Broline-Crowe-Isaacs, and by Baur-Marsh. In this article, we introduce a new type of matrix for any infinite frieze pattern. This approach allows us to give a new proof of the frieze determinant result given by Baur-Marsh.

arXiv commentIn the new version, we explain the relation of our work to the determinant result of Baur and Marsh (BM12 arXiv:1008.5329) and to the work of Holm and Jorgensen (HJ arXiv:2212.11723)