Connection between bi snomial coefficients and their analogs and symmetric functions

Abstract

In this paper, on one hand, we propose a new type of symmetric function to interpret the bi s nomial coefficientsand their analogs. On other hand, according to this function, we give an interpretation of these coefficients by latticepaths and tiling. Some identities of these coefficients are also established. This work is an extension of the results ofBelbachir and Benmezai’s “A q -analogue for bi s nomial coefficients and generalized Fibonacci sequences”.