# Catalan tables and a recursion relation in noncommutative quantum field theory

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.

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