Non-crossing partitions and parking functions: categorification using quiver representations

Claus Michael Ringel (Bielefeld)

Abstract: The lattice of non-crossing partitions is a combinatorial structure which is used in algebra and geometry, but even in probability theory. In 1997, Stanley has constructed a bijection between maximal chains of non-crossing partitions and parking functions. According to Ingalls and Thomas (2006), the lattice of non-crossing partitions can be identified with the lattice of thick subcategeories of the category of representations of the linearly directed quiver Q of type A_n, thus the maximal chains of non-crossing partitions correspond bijectively to the complete exceptional sequences. We will describe Stanley's bijection in terms of the representation theory of the quiver Q.


Ringel
Last modified: Dec 1, 2014