Computational study of non-unitary partitions
Document Type
Article
Publication Date
1-1-2023
Abstract
Following Cayley, MacMahon, and Sylvester, define a non-unitary partition to be an integer partition with no part equal to one, and let ν(n) denote the number of non-unitary partitions of size n. In a 2021 paper, the sixth author proved a formula to compute p(n) by enumerating only non-unitary partitions of size n, and recorded a number of conjectures regarding the growth of ν(n) as n → ∞. Here we refine and prove some of these conjectures. For example, we prove p(n) ∼ ν(n) pn/ζ(2) as n → ∞, and give Ramanujan-like congruences between p(n) and ν(n) such as p(5n) ≡ ν(5n) (mod 5).
Publication Title
Journal of the Ramanujan Mathematical Society
Recommended Citation
Akande, A.,
Genao, T.,
Haag, S.,
Hendon, M.,
Pulagam, N.,
Schneider, R.,
&
Sills, A.
(2023).
Computational study of non-unitary partitions.
Journal of the Ramanujan Mathematical Society,
38(2), 121-128.
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/365