On Minimal Generating Sets of Certain Subsemigroups of Isometries

Authors : Leyla Bugay, Melek Yağci

Pages : 71-78

Doi:10.36753/mathenot.723297

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Publication Date : 2020-10-15

Article Type : Research

Abstract :Let $DP_{n}$ and $ODP_{n}$ be the semigroups of all isometries and of all order-preserving isometries on $X_{n}$, respectively. In this paper we investigate the structure of minimal generating sets of the subsemigroup $DP_{n,r}$= {α ∈ DPn : |im (α)| ≤ r} (similarly of the subsemigroup $ODP_{n,r}$ = {α ∈ ODPn : |im (α)| ≤ r}) for 2 ≤ r ≤ n − 1.                                                                                                                                                                                .
Keywords : Isometry, order-preserving /order-reversing map, (minimal) generating set