Combinatorial Unification of Binomial-Like Arrays

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.