Congruence Relations Mod 2 For (2 x 4^t + 1)-Colored Partitions

Author

Nicholas TorelloFollow

Date of Award

Spring 2019

Degree Type

Thesis

Department

Mathematics

Director of Thesis

Matthew Boylan

First Reader

Alexander Duncan

Second Reader

Alexander Duncan

Abstract

Let p_r(n) denote the difference between the number of r-colored partitions of n into an even number of distinct parts and into an odd number of distinct parts. Inspired by proofs involving modular forms of the Hirschhorn-Sellers Conjecture, we prove a similar congruence for p_r(n). Using the Jacobi Triple Product identity, we discover a much stricter congruence for p_3(n).

First Page

1

Last Page

9

Recommended Citation

Torello, Nicholas, "Congruence Relations Mod 2 For (2 x 4^t + 1)-Colored Partitions" (2019). Senior Theses. 298.
https://scholarcommons.sc.edu/senior_theses/298

Rights

© 2019, Nicholas Torello