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arXiv · 2305.16688

Partitions into powers of an algebraic number

Vítězslav Kala·Mikuláš Zindulka
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Abstract

We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$ is larger than 1. Further, we show that for $\beta$ satisfying a certain condition, the partition function attains all non-negative integers as values.

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Vítězslav Kala, Mikuláš Zindulka. 2023-05-26. Partitions into powers of an algebraic number. https://doi.org/10.1007/s11139-024-00845-2

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