Generalizations of two identities of Guo and Yang

Abstract

In this paper, we provide generalizations of two identities of Guo and Yang [2] for the q-binomial coefficients. This approach allows us to derive new convolution identities for the complete and elementary symmetric functions. New identities involving q-binomial coefficients are obtained as very special cases of these results. A new relationship between restricted partitions and restricted partitions into parts of two kinds is derived in this context.

Mathematics Subject Classification (2010): 05E05, 05A10, 05A19, 95A30, 11B65.

Keywords: Symmetric functions, convolutions, q-binomial coefficient