Combinatorial Unification of Binomial-Like Arrays

Author

James Stephen Lindsay, University of Tennessee - Knoxville

Date of Award

5-2010

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Carl G. Wagner

Committee Members

Pavlos Tzermias, Xia Chen, Gina Pighetti

Abstract

This research endeavors to put a common combinatorial ground under several binomiallike arrays, including the binomial coefficients, q-binomial coefficients, Stirling numbers, q-Stirling numbers, cycle numbers, and Lah numbers, by employing symmetric polynomials and related words with specialized alphabets as well as a balls-and-urns counting approach. Using the method of statistical generating functions, q- and p; q-generalizations of the binomial coefficients, Stirling numbers, cycle numbers, and Lah numbers are all discussed as well, unified under a single general triangular array that is herein referred to as the array of Comtet-Lancaster numbers.

Recommended Citation

Lindsay, James Stephen, "Combinatorial Unification of Binomial-Like Arrays. " PhD diss., University of Tennessee, 2010.
https://trace.tennessee.edu/utk_graddiss/723