Combinatorics and field theory

TL;DR

This paper demonstrates how quantum field theories can be constructed to generate specific integer sequences through their Feynman rules, introducing a novel approach linking combinatorics, graph theory, and physics.

Contribution

It presents a new method for representing combinatorial sequences via quantum field theories, expanding the tools available for combinatorial and graph-theoretic research.

Findings

Constructed quantum field theories for arbitrary integer sequences

Illustrated the method with Stirling numbers

Proposed a new interdisciplinary approach

Abstract

For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph theory.