A Matrix-Based Approach to Combinatorial Identities Involving Binomial Coefficients and Stirling Numbers
GONCA KIZILASLAN *
Department of Mathematics, Faculty of Engineering and Natural Sciences, Kırıkkale University, TR-71450, Kırıkkale, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we present a novel approach to matrix representation. By employing the derivative method of a matrix defined through shift matrices, we show how the sums of specific combinatorial sequences, including binomial coefficients and Stirling numbers, can be directly computed.
Keywords: Matrix equations and identities, combinatorial identities, binomial coefficients, stirling numbers