A binomial Laurent phenomenon algebra associated to the complete graph
Stella Gastineau, Gwyneth Moreland
TL;DR
This paper characterizes the exchange graph of a specific binomial Laurent phenomenon algebra linked to the complete graph, showing it is isomorphic to a known linear Laurent phenomenon algebra's exchange graph.
Contribution
It establishes an isomorphism between the exchange graph of the binomial Laurent phenomenon algebra and that of the linear Laurent phenomenon algebra for complete graphs.
Findings
The exchange graph of the binomial Laurent phenomenon algebra is isomorphic to that of the linear Laurent phenomenon algebra.
Provides a detailed structural understanding of the algebra associated with complete graphs.
Connects two classes of Laurent phenomenon algebras through their exchange graphs.
Abstract
In this paper we find the exchange graph of the rank n binomial Laurent phenomenon algebra associated to the complete graph on n vertices. More specifically, we prove that this exchange graph is isomorphic to that of the rank n linear Laurent phenomenon algebra associated to the complete graph on n vertices discussed in arxiv.org/abs/1206.2612.
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