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arXiv · 2609.08799

A study of $m$-ary partitions whose conjugates are $q$-ary

Geoffrey D. Dietz·Timothy B. Flowers·Shannon R. Lockard
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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.

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Geoffrey D. Dietz, Timothy B. Flowers, Shannon R. Lockard. 2026-09-08. A study of $m$-ary partitions whose conjugates are $q$-ary. https://doi.org/10.13069/jacodesmath.v13i3.393

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