Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions, Nicholas Torello
Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions, Nicholas Torello
Senior Theses
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).