Long mutation cycles

2023/04/23 by Sergey Fomin, Scott Neville, Fomin, Sergey +1
Biochemistry, Genetics and Molecular Biology · Immunology and Microbiology · #05C20 #13F60 #Combinatorics (math.CO) #FOS: Mathematics #HIV Research and Treatment #Protein Degradation and Inhibitors #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.2304.11505

openalex publication_date 2023/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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≥ 4, we describe arbitrarily long mutation cycles involving n-vertex quivers. Each of these mutation cycles allows for an arbitrary choice of n \choose 2 positive integer parameters. None of the mutation cycles we construct can be paved by short mutation cycles.

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