The Decomposition Algorithm for Skew-Symmetrizable Exchange Matrices

  title={The Decomposition Algorithm for Skew-Symmetrizable Exchange Matrices},
  author={Weiwen Gu},
  journal={Electron. J. Comb.},
  • Weiwen Gu
  • Published 2 February 2012
  • Mathematics
  • Electron. J. Comb.
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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