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
Journal	Ramanujan Journal
DOIs	https://doi.org/10.1007/s11139-023-00780-8
State	Accepted/In press - 2023

Keywords

Integer compositions
Integer partitions
Modular forms
Theta functions

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10.1007/s11139-023-00780-8

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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 = "Integer compositions, Integer partitions, Modular forms, Theta functions",

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AU - Sills, Andrew V.

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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.

KW - Integer compositions

KW - Integer partitions

KW - Modular forms

KW - Theta functions

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DO - 10.1007/s11139-023-00780-8

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SN - 1382-4090

JO - Ramanujan Journal

JF - Ramanujan Journal

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Composition-theoretic series in partition theory

Abstract

Keywords

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