Date of Award
2011
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Abstract
Counting lattice paths where the number of occurrences of a given pattern is monitored requires a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of ! and " steps determine the recursion formula. In the case of ballot paths, that is paths the stay weakly above the line y = x, the solutions to the recursions are typically polynomial sequences. The objects of Finite Operator Calculus are polynomial sequences, thus the theory can be used to solve the recursions. The theory of Finite Operator Calculus is strengthened and extended to the multivariate setting in order to obtain solutions, and to prepare for future applications.
Extent
vii, 91 p. : ill.
Recommended Citation
Sullivan, Shaun, "Multivariate finite operator calculus applied to counting ballot paths containing patterns [electronic resource]" (2011). Electronic Theses and Dissertations 2010 - 2019. 342.
https://digitalcommons.fau.edu/etd_general_6/342
Identifier
FADT3174076
Comments
by Shaun Sullivan.|Thesis (Ph.D.)--Florida Atlantic University, 2011.|Includes bibliography.|Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.|by Shaun Sullivan.