Nested Catalan tables and a recurrence relation in noncommutative quantum field theory

Abstract

Correlation functions in a dynamic quartic matrix model are obtained from the twopoint function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These “nested Catalan tables” have a description as diagrams of non-crossing chords and threads.