Maximal green sequences of skew-symmetrizable 3x3 matrices

2012/07/26 by Ahmet Seven, Seven, Ahmet · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1207.6265

openalex publication_date 2012/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Maximal green sequences are particular sequences of mutations which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. In this paper, we show that skew-symmetrizable 3x3 matrices with a mutation-cyclic diagram do not have any maximal green sequences. We also obtain some properties of maximal green sequences of skew-symmetrizable 3x3 matrices with mutation-acyclic diagrams.

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• Sign-coherence and tropical sign pattern for rank 3 real cluster-cyclic exchange matrices

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