On relative ranks of finite transformation semigroups with restricted range

  • I. Dimitrova South-West University “Neofit Rilski”, Blagoevgrad, Bulgaria https://orcid.org/0000-0002-6078-5968
  • J. Koppitz Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Sofia, Bulgaria
Keywords: transformation semigroups with restricted range, orderpreserving transformations, orientation-preserving transformations, relative rank, relative generating sets

Abstract

UDC 512.5

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

 

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Published
24.05.2021
How to Cite
Dimitrova, I., and J. Koppitz. “On Relative Ranks of Finite Transformation Semigroups With Restricted Range”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 5, May 2021, pp. 617 -26, doi:10.37863/umzh.v73i5.288.
Section
Research articles