English

The Decomposition Algorithm of Skew-symmetrizable Exchange Matrices

Combinatorics 2012-02-07 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1202.0529,
  title  = {The Decomposition Algorithm of Skew-symmetrizable Exchange Matrices},
  author = {Weiwen Gu},
  journal= {arXiv preprint arXiv:1202.0529},
  year   = {2012}
}

Comments

arXiv admin note: text overlap with arXiv:1006.4276

R2 v1 2026-06-21T20:14:00.123Z