Composition-theoretic series in partition theory
Document Type
Article
Publication Date
1-1-2023
Department
Department of Mathematical Sciences
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.
Publication Title
Ramanujan Journal
Recommended Citation
Schneider, R.,
&
Sills, A.
(2023).
Composition-theoretic series in partition theory.
Ramanujan Journal.
http://doi.org/10.1007/s11139-023-00780-8
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/120