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 - Sep 15 2023

Scopus Subject Areas

Algebra and Number Theory

Keywords

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

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10.1007/s11139-023-00780-8

Cite this

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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.

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KW - 11P82

KW - Integer compositions

KW - Integer partitions

KW - Modular forms

KW - Theta functions

UR - https://www.scopus.com/pages/publications/85171478331

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Composition-theoretic series in partition theory

Abstract

Scopus Subject Areas

Keywords

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