Contents

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A Combinatorial Interpretation of the Lucas-Nomial Coefficients in Terms of Tiling of Rectangular Boxes

M. Dziemiaticzuk1
1Institute of Informatics, University of Gdazisk, PL-80-952 Gdarisk, Wita Stwosza 57, Poland

Abstract

Generalized binomial coefficients are considered. The aim of this paper is to provide a new general combinatorial interpretation of the Lucas-nomial and (p,q)-nomial coefficients in terms of tiling of d-dimensional rectangular boxes. The recurrence relation of these numbers is proved in a combinatorial way. To this end, our results are extended to the case of corresponding multi-nomial coefficients.