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

  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.},
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… 

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