Master of Science (MS)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
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.
Catalan Numbers; Divisibility; Mersenne Numbers
Bobrowski, Jacob, "Generalized Catalan Numbers and Some Divisibility Properties" (2015). UNLV Theses, Dissertations, Professional Papers, and Capstones. 2518.