Award Date

December 2015

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Peter Shiue

Second Committee Member

Arthur Baragar

Third Committee Member

Derrick DuBose

Fourth Committee Member

David Beisecker

Number of Pages

35

Abstract

I investigate the divisibility properties of generalized Catalan numbers by ex-

tending known results for ordinary Catalan numbers to their general case. First, I define the general Catalan numbers and provide a new derivation of a known formula. Second, I show several combinatorial representations of generalized Catalan numbers and survey bijections across these representation. Third, I extend several divisibility results proved by Koshy. Finally, I prove conditions under which sufficiently large primes form blocks of divisibility and indivisibility of the generalized Catalan numbers, extending a known result by Alter and Kubota.

Keywords

Catalan Numbers; Divisibility; Mersenne Numbers

Disciplines

Mathematics

Language

English


Included in

Mathematics Commons

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