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 coecients, q-binomial coecients, 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 coecients, Stirling numbers, cycle numbers, and Lah numbers are all discussed as well, uni ed under a single general triangular array that is herein referred to as the array of Comtet-Lancaster numbers.

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