Work

Snake Graphs for Graph LP Algebras

Year: 2023

Type: preprint

Abstract: Graph LP algebras are a generalization of cluster algebras introduced by Lam and Pylyavskyy. We provide a combinatorial proof of positivity for certain cluster variables in these algebras. This proof uses a hypergraph generalization of snake graphs, a class of planar graphs which were used by Musiker, Schiffler, and Williams to prove positivity for cluster algebras from surfaces. These results extend those given in our previous paper, where we used a related combinatorial object known as a $T$-path.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2312.12313

Authors: Banaian, Esther, Chepuri, Sunita, Kelley, Elizabeth, Zhang, Sylvester W.

Institutions: Aarhus University, University of Puget Sound, University of Illinois Urbana-Champaign

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: RTG: Research in Combinatorics, RTG: Combinatorics and Algebra, Cluster Algebras, the Ising Model, and Affine Kazhdan-Lusztig Cells

OpenAlex ID: W4390051446

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