• DOI:10.1142/S0218196713400079
• Corpus ID: 14722555

The discrete Fundamental Group of the Associahedron, and the Exchange Module

@article{Barcelo2010TheDF,
  title={The discrete Fundamental Group of the Associahedron, and the Exchange Module},
  author={H{\'e}l{\`e}ne Barcelo and Christopher Severs and Jacob Aaron White},
  journal={Int. J. Algebra Comput.},
  year={2010},
  volume={23},
  pages={745-762}
}

• H. Barcelo, Christopher Severs, J. White
• Published 13 December 2010
• Mathematics, Computer Science
• Int. J. Algebra Comput.

The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We approach the associahedron from the point of view of discrete homotopy theory. We study the abelianization of the discrete fundamental group, and show that it is free abelian of rank . We also find a combinatorial description for a basis of this rank. We also introduce the exchange module of the type An cluster algebra, used to model the relations in the cluster algebra. We use the discrete fundamental group to the study of exchange module, and show that it is also free abelian of rank .