Powers of a Matrix and Combinatorial Identities

In this article we obtain a general polynomial identity in $k$ variables, where $k\geq 2$ 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

Country

United States

Related Organizations

Indian Statistical Institute
India
West Chester University
United States

Keywords

05A19, powers of matrices, Number Theory, FOS: Mathematics, polynomial identity, Mathematics - Combinatorics, Combinatorics (math.CO), Matrices, determinants in number theory, Factorials, binomial coefficients, combinatorial functions, Polynomials in number theory

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