On a Quantum Form of the Binomial Coefficient

A unique form of the quantum binomial coefficient (n choose k) for k = 2 and 3 is presented in this thesis. An interesting double summation formula with floor function bounds is used for k = 3. The equations both show the discrete nature of the quantum form as the binomial coefficient is partitioned into specific quantum integers. The proof of these equations has been shown as well. The equations show that a general form of the quantum binomial coefficient with k summations appears to be feasible. This will be investigated in future work.