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arXiv · 2607.23301

On the automorphisms of numerical power monoids

Anwita Bhowmik·Salvatore Tringali
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Abstract

Let $H$ be a numerical monoid, that is, a cofinite submonoid of $\mathbb N$ (the non-negative integers under addition). Denote by $\mathcal P_{\text{fin},0}(H)$ the monoid obtained by endowing the family of all finite subsets of $H$ containing $0$ with the operation of setwise addition induced by $H$ on its power set. Tringali and Yan [JCTA, 2025] have recently established that $\mathcal P_{\text{fin},0}(\mathbb N)$ has a unique non-trivial automorphism, and conjectured that the automorphism group of $\mathcal P_{\text{fin},0}(H)$ is trivial whenever $H \ne \mathbb N$. We prove this conjecture and, as a byproduct, give a new proof of the Tringali--Yan theorem.

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Anwita Bhowmik, Salvatore Tringali. 2026-07-25. On the automorphisms of numerical power monoids. https://arxiv.org/abs/2607.23301

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