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arXiv · 2006.07724

On relative ranks of finite transformation semigroups with restricted range

Ilinka Dimitrova·Jörg Koppitz
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Abstract

In this paper, we determine the relative rank of the semigroup $T(X,Y)$ of all transformations on a finite chain $X$ with restricted range $Y \subseteq X$ modulo the set $OP(X,Y)$ of all orientation-preserving transformation in $T(X,Y)$. Moreover, we state the relative rank of the semigroup $OP(X,Y)$ modulo the set $O(X,Y)$ of all order-preserving transformations in $OP(X,Y)$. In both cases we characterize the minimal relative generating sets.

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Ilinka Dimitrova, Jörg Koppitz. 2020-06-13. On relative ranks of finite transformation semigroups with restricted range. https://doi.org/10.1007/s11253-021-01955-6

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