The Decomposition Algorithm of Skew-symmetrizable Exchange Matrices [article]

Weiwen Gu
2012 arXiv   pre-print
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 WG. As a corollary, we use this algorithm to determine if a given skew-symmetrizable matrix has finite mutation type.
arXiv:1202.0529v2 fatcat:4xos2i54eva5lpy6r3iffhfky4