Beyond the Laurent phenomenon
Andrei Zabolotskii
Abstract
In a cluster algebra, a subset of initial cluster variables can be specialised in such a way that all elements of the resulting algebra become polynomial in the remaining variables.
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Beyond the Laurent phenomenon
Authors
Andrei Zabolotskii
Abstract
In a cluster algebra, a subset of initial cluster variables can be specialised in such a way that all elements of the resulting algebra become polynomial in the remaining variables.
Paper Structure
This paper contains 4 sections, 5 theorems, 5 equations.
Table of Contents
Key Result
Theorem 1
In a partially labelled quiver associated with a specialised cluster algebra $\left.\mathcal{A}_Q\right|_\sigma$, a vertex is polyamorous if and only if its neighbourhood is a polycule.
Theorems & Definitions (20)
- Example 1: the cluster algebra of type $A_2$
- Definition 1
- Remark 1: motivation for Definition \ref{['def:spec']}
- Remark 2
- Definition 2
- Definition 3
- Theorem 1
- proof
- Remark 3
- Corollary 1
- ...and 10 more