On Minimal Generating Sets of Certain Subsemigroups of Isometries

Let DPn and ODPn be the semigroups of all isometries and of all order-preserving isometries on Xn, respectively. In this paper we investigate the structure of minimal generating sets of the subsemigroup DPn,r = {α ∈ DPn : |im (α)| ≤ r} (similarly of the subsemigroup ODPn,r = {α ∈ ODPn : |im (α)| ≤ r}) for 2 ≤ r ≤ n − 1.

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[1] Al-Kharousi, F., Kehinde, R., Umar, A.: On the semigroup of partial isometries of a finite chain. Comm. Algebra. 44, 639–647 (2016).
[2] Bugay, L., Ya ˘gcı M., Ayık, H.: The ranks of certain semigroups of partial isometries. Semigroup Forum. 97, 214–222 (2018).
[3] Ganyushkin, O., Mazorchuk, V.: Classical finite transformation semigroups. Springer-Verlag. London (2009).
[4] Howie, J. M.: Fundamentals of semigroup theory. Oxford University Press. New York (1995).
[5] Wilson, R.J., Watkins, J.J.: Graphs, An Introductory Approach, A First Course in Discrete Mathematics. Jon Wiley & Sons Inc. Toronto (1990

Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

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