Identities containing Gaussian binomial coefficients

Identities with squares of binomial coefficients

This paper introduces a method for finding closed forms for certain sums involving squares of binomial coefficients. We use this method to present an alternative approach to a problem of evaluating a different type of sums containing squares of the numbers from Catalan's triangle.

Some Identities involving the Partial Sum of q-Binomial Coefficients

We give some identities involving sums of powers of the partial sum of q-binomial coefficients, which are q-analogues of Hirschhorn’s identities [Discrete Math. 159 (1996), 273–278] and Zhang’s identity [Discrete Math. 196 (1999), 291–298].

Projective Geometry over and the Gaussian Binomial Coefficients

1. INTRODUCTION. There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and algebra, but it is rarely discussed as such. The purpose of this article is to bring it to the attention of a broader audience, as the solution to ...

On the q - log - Concavity of Gaussian Binomial Coefficients 335

We give a combinatorial proof that k l-k-1 l + t q q q q a polynomial in q with nonnegative coefficients for nonnegative integers a, b, k, lwith a>~b and l~>k. In particular, for a=b=n and l=k, this implies the q-log-concavity of the Gaussian binomial coefficients k , which was conjectured q by BUTLER (Proc.

Binomial Sums and Identities