Year 2020, Volume 8 , Issue 2, Pages 71 - 78 2020-10-15

On Minimal Generating Sets of Certain Subsemigroups of Isometries

Leyla BUGAY [1] , Melek YAĞCI [2]


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.                                                                                                                                                                               .
Isometry, order-preserving /order-reversing map, (minimal) generating set
  • [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).
Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Orcid: 0000-0002-8316-2763
Author: Leyla BUGAY (Primary Author)
Institution: ÇUKUROVA ÜNİVERSİTESİ MATEMATİK BÖLÜMÜ
Country: Turkey


Orcid: 0000-0002-0457-156X
Author: Melek YAĞCI
Institution: Çukurova Üniversitesi Matematik Bölümü
Country: Turkey


Dates

Publication Date : October 15, 2020

Bibtex @research article { mathenot723297, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {71 - 78}, doi = {10.36753/mathenot.723297}, title = {On Minimal Generating Sets of Certain Subsemigroups of Isometries}, key = {cite}, author = {Bugay, Leyla and Yağcı, Melek} }
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 . DOI: 10.36753/mathenot.723297
MLA Bugay, L , Yağcı, M . "On Minimal Generating Sets of Certain Subsemigroups of Isometries" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 71-78 <https://dergipark.org.tr/en/pub/mathenot/issue/57179/723297>
Chicago Bugay, L , Yağcı, M . "On Minimal Generating Sets of Certain Subsemigroups of Isometries". Mathematical Sciences and Applications E-Notes 8 (2020 ): 71-78
RIS TY - JOUR T1 - On Minimal Generating Sets of Certain Subsemigroups of Isometries AU - Leyla Bugay , Melek Yağcı Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.723297 DO - 10.36753/mathenot.723297 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 71 EP - 78 VL - 8 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.723297 UR - https://doi.org/10.36753/mathenot.723297 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes On Minimal Generating Sets of Certain Subsemigroups of Isometries %A Leyla Bugay , Melek Yağcı %T On Minimal Generating Sets of Certain Subsemigroups of Isometries %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 2 %R doi: 10.36753/mathenot.723297 %U 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
AMA Bugay L , Yağcı M . On Minimal Generating Sets of Certain Subsemigroups of Isometries. Math. Sci. Appl. E-Notes. 2020; 8(2): 71-78.
Vancouver Bugay L , Yağcı M . On Minimal Generating Sets of Certain Subsemigroups of Isometries. Mathematical Sciences and Applications E-Notes. 2020; 8(2): 71-78.
IEEE L. Bugay and M. Yağcı , "On Minimal Generating Sets of Certain Subsemigroups of Isometries", Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, pp. 71-78, Oct. 2020, doi:10.36753/mathenot.723297