Generating New Partition Identities via a Generalized Continued Fraction Algorithm

TL;DR

This paper introduces a method using a generalized continued fraction algorithm to generate numerous new identities related to subsets of integer partitions, expanding the understanding of partition identities.

Contribution

The paper presents a novel approach employing the slow triangle map to systematically produce new partition identities, a significant advancement over previous ad hoc methods.

Findings

Successfully generates multiple new partition identities

Demonstrates the effectiveness of the slow triangle map in partition theory

Provides a framework for future identity discovery

Abstract

Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer partitions.