On Minimal Generating Sets of Certain Subsemigroups of Isometries

Year 2020, Volume: 8 Issue: 2, 71 - 78, 15.10.2020

Leyla Bugay , Melek Yağcı

https://doi.org/10.36753/mathenot.723297

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

References

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