Powers of a matrix and combinatorial identities

Abstract

In this article we obtain a general polynomial identity in $k$ variables, where $k\ge 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k\times k$ matrix. Finally, we use these results to derive various combinatorial identities.

9 pages

Cited by in corpus (2)

• Some Observations on Khovanskii's Matrix Methods for extracting Roots of Polynomials
• Combinatorialization of Sury and McLaughlin identities, general linear recurrences in a unified approach