Composition-theoretic series in partition theory
Number Theory
2022-09-16 v2 Combinatorics
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 -gonal numbers; our proofs employ Ramanujan's theta functions. We explore applications to lacunary -series, and to a new class of composition-theoretic Dirichlet series.
Cite
@article{arxiv.2209.06745,
title = {Composition-theoretic series in partition theory},
author = {Robert Schneider and Andrew V. Sills},
journal= {arXiv preprint arXiv:2209.06745},
year = {2022}
}
Comments
15 pages, typographical correction from previous draft, submitted for publication