An analogue to the Witt identity

TL;DR

This paper explores combinatorial and algebraic problems related to a multivariate identity analogous to the Witt identity, extending previous univariate results to a multivariate context.

Contribution

It introduces a multivariate extension of the Witt identity and solves related combinatorial and algebraic problems, advancing the theoretical understanding.

Findings

Extended Witt identity to multivariate case

Solved associated combinatorial problems

Provided algebraic characterizations

Abstract

In this paper we solve combinatorial and algebraic problems associated with a multivariate identity first considered by S. Sherman wich he called an analog to the Witt identity. We extend previous results obtained for the univariante case.