Catalan tables and a recursion relation in noncommutative quantum field theory

Jins de Jong, Alexander Hock, Raimar Wulkenhaar
April 25, 2019
Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recursion relation. This paper gives the explicit solution of the recursion by mapping it bijectively to a combinatorial structure named `Catalan table'. As by-product of the counting of Catalan tables we prove a combinatorial identity for the Catalan numbers. Catalan tables have a neat description as diagrams of non-crossing chords and threads.