A Bijective Proof of a False Theta Function Identity from Ramanujan’s Lost Notebook

Hannah E. Burson

doi:10.1007/s00026-019-00454-7

A Bijective Proof of a False Theta Function Identity from Ramanujan’s Lost Notebook

Hannah E. Burson

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

1 Scopus citations

Abstract

In his lost notebook, Ramanujan listed five identities related to the false theta function: f(q)=∑n=0∞(-1)nqn(n+1)/2.A new combinatorial interpretation and a proof of one of these identities are given. The methods of the proof allow for new multivariate generalizations of this identity. Additionally, the same technique can be used to obtain a combinatorial interpretation of another one of the identities.

Original language	English (US)
Pages (from-to)	579-588
Number of pages	10
Journal	Annals of Combinatorics
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1007/s00026-019-00454-7
State	Published - Nov 1 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

False theta functions
Overpartitions
Partitions

Access

10.1007/s00026-019-00454-7

OpenUrl availability

Full text

Cite this

@article{f0be1672deda4c87b22486d4081ff7ca,

title = "A Bijective Proof of a False Theta Function Identity from Ramanujan{\textquoteright}s Lost Notebook",

abstract = "In his lost notebook, Ramanujan listed five identities related to the false theta function: f(q)=∑n=0∞(-1)nqn(n+1)/2.A new combinatorial interpretation and a proof of one of these identities are given. The methods of the proof allow for new multivariate generalizations of this identity. Additionally, the same technique can be used to obtain a combinatorial interpretation of another one of the identities.",

keywords = "False theta functions, Overpartitions, Partitions",

author = "Burson, {Hannah E.}",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

month = nov,

day = "1",

doi = "10.1007/s00026-019-00454-7",

language = "English (US)",

volume = "23",

pages = "579--588",

journal = "Annals of Combinatorics",

issn = "0218-0006",

publisher = "Birkhauser Verlag Basel",

number = "3-4",

}

TY - JOUR

T1 - A Bijective Proof of a False Theta Function Identity from Ramanujan’s Lost Notebook

AU - Burson, Hannah E.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In his lost notebook, Ramanujan listed five identities related to the false theta function: f(q)=∑n=0∞(-1)nqn(n+1)/2.A new combinatorial interpretation and a proof of one of these identities are given. The methods of the proof allow for new multivariate generalizations of this identity. Additionally, the same technique can be used to obtain a combinatorial interpretation of another one of the identities.

AB - In his lost notebook, Ramanujan listed five identities related to the false theta function: f(q)=∑n=0∞(-1)nqn(n+1)/2.A new combinatorial interpretation and a proof of one of these identities are given. The methods of the proof allow for new multivariate generalizations of this identity. Additionally, the same technique can be used to obtain a combinatorial interpretation of another one of the identities.

KW - False theta functions

KW - Overpartitions

KW - Partitions

UR - http://www.scopus.com/inward/record.url?scp=85074829630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074829630&partnerID=8YFLogxK

U2 - 10.1007/s00026-019-00454-7

DO - 10.1007/s00026-019-00454-7

M3 - Article

AN - SCOPUS:85074829630

SN - 0218-0006

VL - 23

SP - 579

EP - 588

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 3-4

ER -

A Bijective Proof of a False Theta Function Identity from Ramanujan’s Lost Notebook

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this