Work

Long mutation cycles

Year: 2025

Type: article

Abstract: A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed $$n\ge 4$$ n ≥ 4 , we describe arbitrarily long mutation cycles involving n -vertex quivers. Each of these mutation cycles allows for an arbitrary choice of $$\left( {\begin{array}{c}n\\ 2\end{array}}\right) $$ n 2 positive integer parameters. None of the mutation cycles we construct can be paved by short mutation cycles.

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01090-1

Authors: Sergey Fomin, Scott Neville

Institution: University of Michigan

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: National Science Foundation