A Combinatorial Approach for q-Analogue of r-Stirling Numbers
Roberto B. Corcino *
Department of Mathematics, Mindanao State University Marawi City, Philippines 9700, Philippines.
Jezer C. Fernandez
Department of Mathematics, Mindanao State University Marawi City, Philippines 9700, Philippines.
*Author to whom correspondence should be addressed.
Abstract
We define a q-analogue of r-Stirling numbers of the second kind using their combinatorial interpretation in terms of set partition. Some properties are obtained including recurrence relation, explicit formula and certain symmetric formula. Moreover, a q-analogue of r-Stirling numbers of the first kind is introduced to obtain a q-analogue of the orthogonality and inverse relations of the two kinds of r-Stirling numbers.
Keywords: Stirling numbers, r-Stirling Numbers, q-binomial coefficients, q-factorial