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arXiv · 2102.03118

On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range

Ilinka Dimitrova·Jörg Koppitz
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Abstract

Let $X$ be an infinite linearly ordered set and let $Y$ be a nonempty subset of $X$. We calculate the relative rank of the semigroup $OP(X,Y)$ of all orientation-preserving transformations on $X$ with restricted range $Y$ modulo the semigroup $O(X,Y)$ of all order-preserving transformations on $X$ with restricted range $Y$. For $Y = X$, we characterize the relative generating sets of minimal size.

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Ilinka Dimitrova, Jörg Koppitz. 2021-02-05. On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range. https://doi.org/10.1080/00927872.2021.2000998

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