On Some Generalizations via Multinomial Coefficients
Mahid M. Mangontarum *
Department of Mathematics, Mindanao State University-Main Campus, Marawi City, Philippines 9700, Philippines
Najma B. Pendiaman
Department of Mathematics, Mindanao State University-Main Campus, Marawi City, Philippines 9700, Philippines
*Author to whom correspondence should be addressed.
Abstract
This paper gives a brief discussion on the Multinomial coefficients. Using this notion, we obtain generalizations of the Vandermonde’s and the Chu Shih-Chieh’s identities for the Binomial coefficients, respectively. This is done through the use of two known principles in Combinatorics, namely, the Addition and the Multiplication principles. Some examples of generating functions of a sequence involving the multinomial coefficients are also derived and presented.
Keywords: Binomial coefficients, multinomial coefficients, generating functions, q-analogues.