Identities that represent powers of positive integers using multinomial coefficients

TL;DR

This paper introduces new combinatorial identities that express powers of positive integers through multinomial coefficients, distinct from traditional multinomial theorem applications.

Contribution

It presents novel combinatorial identities involving multinomial coefficients that are not derived from standard multinomial theorem or Vandermonde's convolution.

Findings

New identities representing powers of positive integers

Distinct from classical multinomial theorem applications

Contributes to combinatorial mathematics

Abstract

In this paper, we show combinatorial identities that represent powers of positive integers using multinomial coefficients, which do not come from the multinomial theorem and the multinomial Vandermonde's convolution.