Copartitions

Hannah E. Burson; Dennis Eichhorn

doi:10.1007/s00026-022-00607-1

Copartitions

Hannah E. Burson, Dennis Eichhorn

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	519-537
Number of pages	19
Journal	Annals of Combinatorics
Volume	27
Issue number	3
DOIs	https://doi.org/10.1007/s00026-022-00607-1
State	Published - Sep 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Partition summatory function
Partitions
Rogers–Ramanujan functions
Theta functions

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10.1007/s00026-022-00607-1

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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.",

keywords = "Partition summatory function, Partitions, Rogers–Ramanujan functions, Theta functions",

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AU - Burson, Hannah E.

AU - Eichhorn, Dennis

PY - 2023/9

Y1 - 2023/9

N2 - 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.

AB - 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.

KW - Partition summatory function

KW - Partitions

KW - Rogers–Ramanujan functions

KW - Theta functions

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JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 3

ER -

Copartitions

Abstract

Bibliographical note

Keywords

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