Partitions With Distinct Parts and the Parity of Their Rank

Author

John Graf, College of the Holy Cross

Date of Creation

2020

Document Type

Departmental Honors Thesis - Restricted Access

Department

Mathematics

First Advisor

Cristina Ballantine

Abstract

Given a partition λ of n, its rank, r(λ), is equal to the largest part minus the number of parts. We consider partitions of n with distinct parts and investigate the excess, s(n), of the number of such partitions with even rank over those with odd rank. Andrews, Dyson, and Hickerson used the arithmetic of Q(√6) to prove that s(n) = 0 for infinitely many n, and lim sup |s(n)| = +∞. We present work toward toward a combinatorial proof of these results.

Recommended Citation

Graf, John, "Partitions With Distinct Parts and the Parity of Their Rank" (2020). Math and Computer Science Honors Theses. 61.
https://crossworks.holycross.edu/math_honor/61