Biases among classes of rank-crank partitions$\pmod{11}$

TL;DR

This paper proves inequalities among ranks, cranks, and partitions modulo 11, confirming conjectures by Borozenets, and enhances understanding of partition class biases.

Contribution

It establishes new inequalities for partition statistics modulo 11, addressing conjectures and advancing the theoretical framework of partition class biases.

Findings

Proved inequalities among ranks, cranks, and partitions mod 11

Confirmed conjectures posed by Borozenets

Enhanced understanding of partition class biases

Abstract

In this paper, we prove inequalities for ranks, cranks, and partitions among different classes modulo 11. These were conjectured by Borozenets.