Composition-theoretic series in partition theory

Robert Schneider; Andrew V. Sills

doi:10.1007/s11139-023-00780-8

Composition-theoretic series in partition theory

Robert Schneider, Andrew V. Sills

Mathematical Sciences

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

Abstract

We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as sums over compositions into parts that are k-gonal numbers; our proofs employ Ramanujan’s theta functions. We explore applications to lacunary q-series, and to a new class of composition-theoretic Dirichlet series.

Original language	English
Pages (from-to)	1863-1881
Number of pages	19
Journal	Ramanujan Journal
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s11139-023-00780-8
State	Published - Dec 2024

Scopus Subject Areas

Algebra and Number Theory

Keywords

05A17
11P82
Integer compositions
Integer partitions
Modular forms
Theta functions

Access to Document

10.1007/s11139-023-00780-8

Cite this

@article{b386d0d7971248218c253db53ff26f8a,

title = "Composition-theoretic series in partition theory",

abstract = "We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as sums over compositions into parts that are k-gonal numbers; our proofs employ Ramanujan{\textquoteright}s theta functions. We explore applications to lacunary q-series, and to a new class of composition-theoretic Dirichlet series.",

keywords = "05A17, 11P82, Integer compositions, Integer partitions, Modular forms, Theta functions",

author = "Robert Schneider and Sills, {Andrew V.}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.",

year = "2024",

month = dec,

doi = "10.1007/s11139-023-00780-8",

language = "English",

volume = "65",

pages = "1863--1881",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - Composition-theoretic series in partition theory

AU - Schneider, Robert

AU - Sills, Andrew V.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.

PY - 2024/12

Y1 - 2024/12

N2 - We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as sums over compositions into parts that are k-gonal numbers; our proofs employ Ramanujan’s theta functions. We explore applications to lacunary q-series, and to a new class of composition-theoretic Dirichlet series.

AB - We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as sums over compositions into parts that are k-gonal numbers; our proofs employ Ramanujan’s theta functions. We explore applications to lacunary q-series, and to a new class of composition-theoretic Dirichlet series.

KW - 05A17

KW - 11P82

KW - Integer compositions

KW - Integer partitions

KW - Modular forms

KW - Theta functions

UR - http://www.scopus.com/inward/record.url?scp=85171478331&partnerID=8YFLogxK

U2 - 10.1007/s11139-023-00780-8

DO - 10.1007/s11139-023-00780-8

M3 - Article

AN - SCOPUS:85171478331

SN - 1382-4090

VL - 65

SP - 1863

EP - 1881

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 4

ER -

Composition-theoretic series in partition theory

Abstract

Scopus Subject Areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this