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arXiv · 2507.11122

On certain subsemigroups of finite oriented and order-decreasing full transformations

Gonca Ayık·Hayrullah Ayık·Ilinka Dimitrova·Jörg Koppitz
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Abstract

Let $\mathcal{ORD}_{n}$ be the semigroup consisting of all oriented and order-decreasing full transformations on the finite chain $X_{n}=\{ 1<\cdots<n \}$, and for $1\leq r\leq n-1$, let $$\mathcal{ORD}(n,r) =\{\alpha \in \mathcal{ORD}_{n}\, :\, \lvert \textrm{im}(\alpha )\rvert \leq r\}.$$ In this paper, we determine the cardinality of $\mathcal{ORD}(n,r)$ and the number of nilpotent elements of $\mathcal{ORD}(n,r)$, we find a minimal generating set and the rank of $\mathcal{ORD}(n,r)$, and moreover, we characterize all maximal subsemigroups of $\mathcal{ORD}(n,r)$ for each $3\leq r\leq n-1$.

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Gonca Ayık, Hayrullah Ayık, Ilinka Dimitrova, Jörg Koppitz. 2025-07-15. On certain subsemigroups of finite oriented and order-decreasing full transformations. https://doi.org/10.1007/s00233-026-10628-4

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