Date of Award
Mathematics and Statistics
Partitions (Mathematics), Number theory, Generating functions
Partitions are a subject of study in the field of number theory and have been studied extensively since the eighteenth-century mathematician Leonhard Euler's work on them. More famously, Srinivasa Ramanujan was credited for advancing the field of partition theory with his discoveries in the early 1900's. In the late 1960’s, R.F. Churchouse extensively studied congruences of the binary partition function and made many conjectures about their properties, which went unproven for a time. Some of these were soon after proven by Ø. Rødseth and generalized to p-ary partitions where p is a prime number. In 2015, Andrews et al. proved a surprising and entirely unexpected generalization of the m-ary partition function modulo m that utilized generating functions and elementary techniques; this generalization is the focus of this thesis.
Ortiz, Jose A., "Integer Partitions and Why Counting Them is Hard" (2017). University Honors Theses. Paper 365.