DescriptionAn associahedron is an (n-2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters, and the edges correspond to a single application of the associativity rule. The number of its vertices C_n is a Catalan number, an element of one of the most frequently used sequences of natural numbers appearing as an answer to numerous enumerative problems, completely different at the first glance. Associahedra and their generalizations are also central objects in modern theory of cluster algebras connecting numerous fields of mathematics and theoretical physics.PrerequisitesAlgebra IICorequisitesGeometry III or Topology IIIResources:The wikipedia page for Catalan numbers contains many examples of problems where these numbers arise. You could start your reading from "Catalan numbers" by Tom Davis. The following elementary book includes Catalan numbers in a series of other types of distinguished number sequences:
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email: Pavel Tumarkin