On a Quantum Form of the Binomial Coefficient

Author

Eric J. Jacob, University of Tennessee Space InstituteFollow

Date of Award

5-2012

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

K.C. Reddy

Committee Members

Kenneth Kimble, Gary Flandro

Abstract

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.

Recommended Citation

Jacob, Eric J., "On a Quantum Form of the Binomial Coefficient. " Master's Thesis, University of Tennessee, 2012.
https://trace.tennessee.edu/utk_gradthes/1168