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Automorphisms of special egg-box diagrams

It turns out (surprisingly) that the answer to my question is yes, and there are even finite examples. I came up with the following diagram $$ \begin{array}{|c|c|c|c|c|c|} \hline \circ & \circ &...
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On the maximum elements of a numerical semigroup that have order between $n$ and $2n$

Unfortunately, I realize now that I made a typo in the GAP code; the answer is no. Even for $S^* \setminus 2S^* = \{10, 11, 34\},$ there is a counterexample. One can verify that $79 = 1 \cdot 11 + 2 \...
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What are the n-ary subsemigroups of $\mathbb{N}$?

A description is given by: Proposition. Let $L$ be a nonempty $n$-ary subsemigroup of $\mathbf{N}$, and generating $\mathbf{Z}$ as a subgroup. Then there exists $k\ge 1$ dividing $n-1$ and $0<\ell&...
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