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arXiv · 2607.13290

Words don't come easy: strong affine representations of the polycyclic monoids

Kristóf Varga·Tamás Waldhauser
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Abstract

Each one-dimensional strong affine representation of the polycyclic monoid $\mathcal{P}_n$ is induced by a complete system of residues modulo $n$. We completely characterize these representations in the case when the system of residues is an arithmetic sequence. We accomplish this by introducing a closure operator on the set of primitive words over $\{0,1,\dots,n-1\}$, and we also describe the lattice of closed sets. This characterization covers all one-dimensional strong affine representations of $\mathcal{P}_2$.

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Kristóf Varga, Tamás Waldhauser. 2026-07-14. Words don't come easy: strong affine representations of the polycyclic monoids. https://arxiv.org/abs/2607.13290

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