Evaluation of the period of a family of triangle and box ladder graphs

TL;DR

This paper proves a formula for the period of a family of complex ladder graphs with triangles and boxes, linking their evaluation to binomial coefficients and zeta functions, advancing understanding of graph periods in mathematical physics.

Contribution

It introduces a closed-form expression for the periods of a specific family of ladder graphs involving zeta functions and combinatorial coefficients.

Findings

Derived a formula for the period involving binomial coefficients and zeta functions.

Established a connection between graph structure and special mathematical constants.

Provides a basis for further exploration of graph periods in quantum field theory.

Abstract

We prove that the period of a family of $n$ loop graphs with triangle and box ladders evaluates to $\frac{4}{n}\binom{2n-2}{n-1}\zeta(2n-3)$