Toric mutations in the \(\mathrm{dp}_2\) quiver and subgraphs of the \(\mathrm{dp}_2\) brane tiling

zbMath1442.13068arXiv1611.05320MaRDI QIDQ2415081

Lisa Yang, Thuy Duong Vuong, Yibo Gao, Zhaoqi Li

Publication date: 20 May 2019

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05320

Mathematics Subject Classification ID

Representations of quivers and partially ordered sets (16G20) Combinatorial aspects of tessellation and tiling problems (05B45) Directed graphs (digraphs), tournaments (05C20) Cluster algebras (13F60)

Related Items (2)

Discrete dynamics in cluster integrable systems from geometric \(R\)-matrix transformations ⋮ The cluster modular group of the dimer model

Cites Work

• Applications of graphical condensation for enumerating matchings and tilings
• Cluster expansion formulas and perfect matchings
• A graph theoretic expansion formula for cluster algebras of classical type
• Perfect matchings and the octahedron recurrence
• Beyond Aztec castles: toric cascades in the \(dP_3\) quiver
• Brane tilings and specular duality
• Colored BPS pyramid partition functions, quivers and cluster transformations
• A combinatorial formula for rank 2 cluster variables
• Cluster algebras I: Foundations
• Aztec castles and the dP3 quiver

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