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arXiv · 1712.00973

Uniformly column sign-coherence and the existence of maximal green sequences

Peigen Cao·Fang Li
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Abstract

In this paper, we prove that each matrix in $M_{m\times n}(\mathbb Z_{\geq0})$ is uniformly column sign-coherent with respect to any $n\times n$ 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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Peigen Cao, Fang Li. 2017-12-04. Uniformly column sign-coherence and the existence of maximal green sequences. https://arxiv.org/abs/1712.00973

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