Yet another note on notation

TL;DR

This paper introduces a new name and notation for a class of numbers related to Euler, Stirling, Bernoulli, and Fubini, aiming to standardize their recognition and usage in mathematical literature.

Contribution

It proposes a specific name and notation for these historically significant but under-recognized numbers, enhancing clarity and consistency in mathematical references.

Findings

Proposes a new standard notation for these numbers

Provides historical context linking to Euler and other mathematicians

Aims to facilitate broader adoption in mathematical literature

Abstract

Back in 1755, Euler explored an interesting array of numbers that now frequently appears in polynomial identities, combinatorial problems, and finite calculus, among other places. These numbers share a strong connection with well-known number families, such as those of Stirling, Bernoulli, and Fubini. Despite their importance, they often go unnoticed because of the lack of a specific name and standard notation. This paper aims to address this oversight by proposing an appropriate name and notation, aligned with established mathematical conventions, and supported by (we hope) strong enough arguments to facilitate their acceptance from the mathematical community.