Jeong, In-Jee; Musiker, Gregg; Zhang, Sicong Gale-Robinson sequences and brane tilings. (English) Zbl 1294.05016 Proceedings of the 25th international conference on formal power series and algebraic combinatorics, FPSAC 2013, Paris, France, June 24–28, 2013. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 707-718, electronic only (2013). Summary: We study variants of Gale-Robinson sequences, as motivated by cluster algebras with principal coefficients. For such cases, we give combinatorial interpretations of cluster variables using brane tilings, as from the physics literature.For the entire collection see [Zbl 1281.05001]. Cited in 9 Documents MSC: 05A15 Exact enumeration problems, generating functions 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:cluster algebras; principal coefficients; \(F\)-polynomials; Aztec diamonds; Gale-Robinson recurrence; perfect matchings; brane tilings; Seiberg dualities Software:Quiver; SageMath PDFBibTeX XMLCite \textit{I.-J. Jeong} et al., in: Proceedings of the 25th international conference on formal power series and algebraic combinatorics, FPSAC 2013, Paris, France, June 24--28, 2013. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). 707--718 (2013; Zbl 1294.05016) Full Text: Link