Bernoulli Partitions

TL;DR

This paper explores a novel partitioning of Bernoulli numbers into sums of rational numbers with specific properties, revealing new insights into their structure and behavior as n grows large.

Contribution

It introduces a natural partitioning scheme for Bernoulli numbers into sums of same-signed, monotonic rational numbers, expanding understanding of their properties.

Findings

Partitioning scheme for Bernoulli numbers B_{2n} into sums of rational numbers.

Properties of these rational numbers analyzed, especially for large n.

Insights into the structure and limits of Bernoulli number partitions.

Abstract

Scale invariant scattering suggests that all Bernoulli numbers B_{2n} can be naturally partitioned, i.e., written as particular finite sums of same-signed, monotonic, rational numbers. Some properties of these rational numbers are discussed here, especially in the limit of large n.