Plane Partitions and Young Diagrams, q-Catalan Numbers and Their Hankel Determinants

Student: Khadush Dayana

Supervisor: Takashi Takebe

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2017

In this paper, we study one of a q-analogues of the Catalan numbers. By considering plane partitions in the form of Young diagrams, we obtain the connection between the Catalan numbers and the number of three-dimensional Young diagrams in a triangular prism. Using the Lindström-Gessel-Viennot lemma (LGV), which provides a way to compute weights of non-intersecting lattice paths, we will obtain the generating function of these diagrams.

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