On some relations satisfied by the p,q-binomial coefficient

Author:

Mark SHATTUCK

2010 Mathematics Subject Classication:

11B65

Keywords:

binomial coefficient, combinatorial identity, p,q-analogue

Abstract:

We use counting arguments to establish several new relations involving a p,q-analogue of the binomial coefficient as well as provide different proofs of some prior ones. Among the identities and properties we explore are triangular, horizontal, and vertical recurrences, horizontal generating functions, orthogonality relations, and convolutions.

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Shat-2011

Vol. 6 (14), 2011