On the ranks of certain ideals of monotone contractions

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Hacettepe Journal of Mathematics and Statistics
Volume:49 Issue:6
On the ranks of certain ideals of monotone contractions

On the ranks of certain ideals of monotone contractions

Pages : 1988-1996

View : 104 | Download : 16

Publication Date : 2020-12-08

Article Type : Research Paper

Abstract :Let $T_{n}$ be the insert ignore into journalissuearticles values(full); transformation semigroup, and let $OCT_{n}$ and $ORCT_{n}$ be its subsemigroups of isotone contractions and of monotone contractions on a finite chain $X_{n}=\{1,\ldots ,n\}$ under its natural order, respectively. In this study, we obtain the ranks of the ideals $OCT_{n,r}=\{\alpha\in OCT_{n}\,:\, |iminsert ignore into journalissuearticles values(\alpha);|\leq r\}$ and $ORCT_{n,r}=\{ \alpha \in ORCT_{n}\,:\, |iminsert ignore into journalissuearticles values(\alpha);|\leq r\}$ for $1\leq r\leq n-1$.
Keywords : isotone antitone monotone transformation, contraction, rank

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