The dual of Spivey’s bell number identity from Zeon algebra.

Abstract

In this paper, we give a new short proof of the dual of Spivey’s Bell number identity due to Mezo. Our approach follows from basic manipulations involving a fundamental identity representing factorials in the Zeon algebra. This work, along with a previous one due to the author and dos Anjos, shows that Spivey’s and Mez˝o’s identities have at their root a common underlying algebraic origin.