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Year 2020, , 71 - 78, 15.10.2020
https://doi.org/10.36753/mathenot.723297

Abstract

References

  • [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., Yağcı 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).

On Minimal Generating Sets of Certain Subsemigroups of Isometries

Year 2020, , 71 - 78, 15.10.2020
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.                                                                                                                                                                               .

References

  • [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., Yağcı 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).
There are 5 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Leyla Bugay 0000-0002-8316-2763

Melek Yağcı This is me 0000-0002-0457-156X

Publication Date October 15, 2020
Submission Date April 19, 2020
Acceptance Date June 22, 2020
Published in Issue Year 2020

Cite

APA Bugay, L., & Yağcı, M. (2020). On Minimal Generating Sets of Certain Subsemigroups of Isometries. Mathematical Sciences and Applications E-Notes, 8(2), 71-78. https://doi.org/10.36753/mathenot.723297
AMA Bugay L, Yağcı M. On Minimal Generating Sets of Certain Subsemigroups of Isometries. Math. Sci. Appl. E-Notes. October 2020;8(2):71-78. doi:10.36753/mathenot.723297
Chicago Bugay, Leyla, and Melek Yağcı. “On Minimal Generating Sets of Certain Subsemigroups of Isometries”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 71-78. https://doi.org/10.36753/mathenot.723297.
EndNote Bugay L, Yağcı M (October 1, 2020) On Minimal Generating Sets of Certain Subsemigroups of Isometries. Mathematical Sciences and Applications E-Notes 8 2 71–78.
IEEE L. Bugay and M. Yağcı, “On Minimal Generating Sets of Certain Subsemigroups of Isometries”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 71–78, 2020, doi: 10.36753/mathenot.723297.
ISNAD Bugay, Leyla - Yağcı, Melek. “On Minimal Generating Sets of Certain Subsemigroups of Isometries”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 71-78. https://doi.org/10.36753/mathenot.723297.
JAMA Bugay L, Yağcı M. On Minimal Generating Sets of Certain Subsemigroups of Isometries. Math. Sci. Appl. E-Notes. 2020;8:71–78.
MLA Bugay, Leyla and Melek Yağcı. “On Minimal Generating Sets of Certain Subsemigroups of Isometries”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 71-78, doi:10.36753/mathenot.723297.
Vancouver Bugay L, Yağcı M. On Minimal Generating Sets of Certain Subsemigroups of Isometries. Math. Sci. Appl. E-Notes. 2020;8(2):71-8.

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