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

## TL;DR

This paper introduces nested Catalan tables, a new combinatorial structure linked to correlation functions in noncommutative quantum field theory, providing explicit solutions to recurrence relations via Catalan numbers.

## Contribution

It presents the first explicit solution to a recurrence relation in quantum field theory using nested Catalan tables, connecting combinatorics with physics.

## Key findings

- Explicit solution to the recurrence relation
- Nested Catalan tables counted by Catalan numbers
- Diagrammatic representation as non-crossing chords and threads

## Abstract

Correlation functions in a dynamic quartic matrix model are obtained from the two-point 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.