The Decomposition Algorithm of Skew-symmetrizable Exchange Matrices

Details The Decomposition Algorithm of Skew-symmetrizable Exchange Matrices The Decomposition Algorithm of Skew-symmetrizable Exchange Matrices

2012-02-02

arxiv.org/abs/1202.0529v2

Mathematics

Combinatorics

arXiv admin note: text overlap with arXiv:1006.4276

Scientific paper

Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that determines if a given skew-symmetrizable matrix is of such type. This algorithm generalizes the one in \cite{WG}. As a corollary, we use this algorithm to determine if a given skew-symmetrizable matrix has finite mutation type.

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