Date of Award
Doctor of Philosophy
Carl G. Wagner
Pavlos Tzermias, Xia Chen, Gina Pighetti
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.
Lindsay, James Stephen, "Combinatorial Unification of Binomial-Like Arrays. " PhD diss., University of Tennessee, 2010.