Biases in Non-Unitary Partitions
Number Theory
2026-01-12 v2 Combinatorics
Abstract
Recently, the concept of parity bias in integer partitions has been studied by several authors. We continue this study here, but for non-unitary partitions (namely, partitions with parts greater than ). We prove analogous results for these restricted partitions to those that have been obtained by Kim, Kim, and Lovejoy (2020) and Kim and Kim (2021). We also look at inequalities between two classes of partitions studied by Andrews (2019), where the parts are separated by parity (either all odd parts are smaller than all even parts or vice versa).
Keywords
Cite
@article{arxiv.2301.09845,
title = {Biases in Non-Unitary Partitions},
author = {Pankaj Jyoti Mahanta and Manjil P. Saikia and Abhishek Sarma},
journal= {arXiv preprint arXiv:2301.09845},
year = {2026}
}
Comments
11 pages, accepted in Bolet\'in de la Sociedad Matem\'atica Mexicana