Copartitions
Hannah E. Burson, Dennis Eichhorn

TL;DR
This paper introduces the theory of copartitions, a generalization of partitions, connecting to various classical topics in partition theory and providing new generating functions through analytic and combinatorial methods.
Contribution
It develops the foundational theory of copartitions and presents novel three-parameter generating functions with potential broad implications in partition theory.
Findings
Derived two forms of the three-parameter generating function
Connected copartitions to Rogers-Ramanujan and mock theta functions
Explored special cases demonstrating broader impact
Abstract
We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions, theta functions, mock theta functions, partitions with parts separated by parity, and crank statistics. Using both analytic and combinatorial methods, we give two forms of the three-parameter generating function, and we study several special cases that demonstrate the potential broader impact the study of copartitions may have.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research
