Uniformly column sign-coherence and the existence of maximal green sequences
Peigen Cao, Fang Li

TL;DR
This paper proves a uniform column sign-coherence property for matrices related to skew-symmetrizable matrices and reduces the problem of finding maximal green sequences to irreducible cases.
Contribution
It introduces the concept of irreducible skew-symmetrizable matrices and links their maximal green sequences to the general case.
Findings
Proves uniform column sign-coherence for a class of matrices.
Defines irreducible skew-symmetrizable matrices.
Reduces maximal green sequence existence to irreducible matrices.
Abstract
In this paper, we prove that each matrix in is uniformly column sign-coherent with respect to any skew-symmetrizable integer matrix. Using such matrices, we introduce the definition of irreducible skew-symmatrizable matrix. Based on this, the existence of a maximal green sequence for a skew-symmetrizable matrices is reduced to the existence of a maximal green sequence for irreducible skew-symmetrizable matrices.
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models
