A study of m-ary partitions whose conjugates are q-ary
Abstract
While people have studied m-ary partitions of an integer n and studied conjugation of partitions of n, these topics are rarely mixed because the m-ary property is almost always lost after conjugation. In a previous work, Flowers and Lockard investigated m-ary partitions of n whose conjugates were also m-ary. We generalize that previous work by studying m-ary partitions whose conjugates are q-ary, where m and q may be distinct. We provide a family of operators on these partitions that can be used to generate all such partitions uniquely and associate a unique polynomial with each partition based on the sequence of operators used to generate it. Using the generating operators and modular arithmetic we explore many examples and families of m-ary partitions whose conjugates are q-ary.
Versions
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BibTeX
@misc{dietz2026study,
title = {{A study of $m$-ary partitions whose conjugates are $q$-ary}},
author = {Geoffrey D. Dietz and Timothy B. Flowers and Shannon R. Lockard},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08799},
eprint = {2609.08799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08799},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A study of m-ary partitions whose conjugates are q-ary
AU - Geoffrey D. Dietz
AU - Timothy B. Flowers
AU - Shannon R. Lockard
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08799
UR - https://arxiv.org/abs/2609.08799
AB - While people have studied m-ary partitions of an integer n and studied conjugation of partitions of n, these topics are rarely mixed because the m-ary property is almost always lost after conjugation. In a previous work, Flowers and Lockard investigated m-ary partitions of n whose conjugates were also m-ary. We generalize that previous work by studying m-ary partitions whose conjugates are q-ary, where m and q may be distinct. We provide a family of operators on these partitions that can be used to generate all such partitions uniquely and associate a unique polynomial with each partition based on the sequence of operators used to generate it. Using the generating operators and modular arithmetic we explore many examples and families of m-ary partitions whose conjugates are q-ary.
ER -