Presentations for subsemigroups of P D n

Abdullahi Umar

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 2, page 417-426
  • ISSN: 0011-4642

Abstract

top
Let [ n ] = { 1 , ... , n } be an n -chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of [ n ] , the semigroup of partial one-to-one order-decreasing mappings of [ n ] , the semigroup of full order-preserving and order-decreasing mappings of [ n ] , the semigroup of partial one-to-one order-preserving and order-decreasing mappings of [ n ] , and the semigroup of partial order-preserving and order-decreasing mappings of [ n ] .

How to cite

top

Umar, Abdullahi. "Presentations for subsemigroups of $PD_n$." Czechoslovak Mathematical Journal 69.2 (2019): 417-426. <http://eudml.org/doc/294869>.

@article{Umar2019,
abstract = {Let $[n]=\lbrace 1,\ldots ,n\rbrace $ be an $n$-chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-decreasing mappings of $[n]$, the semigroup of full order-preserving and order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-preserving and order-decreasing mappings of $[n]$, and the semigroup of partial order-preserving and order-decreasing mappings of $[n]$.},
author = {Umar, Abdullahi},
journal = {Czechoslovak Mathematical Journal},
keywords = {presentation; order-decreasing mapping; order-preserving mapping; transformation semigroups},
language = {eng},
number = {2},
pages = {417-426},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Presentations for subsemigroups of $PD_n$},
url = {http://eudml.org/doc/294869},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Umar, Abdullahi
TI - Presentations for subsemigroups of $PD_n$
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 417
EP - 426
AB - Let $[n]=\lbrace 1,\ldots ,n\rbrace $ be an $n$-chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-decreasing mappings of $[n]$, the semigroup of full order-preserving and order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-preserving and order-decreasing mappings of $[n]$, and the semigroup of partial order-preserving and order-decreasing mappings of $[n]$.
LA - eng
KW - presentation; order-decreasing mapping; order-preserving mapping; transformation semigroups
UR - http://eudml.org/doc/294869
ER -

References

top
  1. Aĭzenštat, A. J., Defining relations of finite symmetric semigroups, Mat. Sb. N.Ser. 45 (1958), 261-280 Russian. (1958) Zbl0081.01901MR0101275
  2. Aĭzenštat, A. J., The defining relations of the endomorphism semigroup of a finite linearly ordered set, Sib. Mat. Zh. 3 (1962), Russian 161-169. (1962) Zbl0114.01702MR0148781
  3. Easdown, D., East, J., FitzGerald, D. G., 10.1142/S0218196708004470, Int. J. Algebra Comput. 18 (2008), 357-374. (2008) Zbl1158.20326MR2403826DOI10.1142/S0218196708004470
  4. East, J., 10.1080/00927870500542689, Commun. Algebra 34 (2006), 1671-1689. (2006) Zbl1099.20029MR2229484DOI10.1080/00927870500542689
  5. East, J., 10.1007/s00233-010-9250-1, Semigroup Forum 81 (2010), 357-379. (2010) Zbl1207.20058MR2678722DOI10.1007/s00233-010-9250-1
  6. East, J., 10.1142/S0218196710005509, Int. J. Algebra Comput. 20 (2010), 1-25. (2010) Zbl1201.20063MR2655913DOI10.1142/S0218196710005509
  7. East, J., 10.1016/j.jalgebra.2011.04.008, J. Algebra 339 (2011), 1-26. (2011) Zbl1277.20069MR2811310DOI10.1016/j.jalgebra.2011.04.008
  8. East, J., 10.1142/S021819671100611X, Int. J. Algebra Comput. 21 (2011), 147-178. (2011) Zbl1229.20066MR2787456DOI10.1142/S021819671100611X
  9. East, J., 10.1007/s00233-012-9447-6, Semigroup Forum 86 (2013), 451-485. (2013) Zbl1273.20065MR3053774DOI10.1007/s00233-012-9447-6
  10. East, J., 10.1007/s00233-013-9512-9, Semigroup Forum 89 (2014), 72-76. (2014) Zbl1304.20074MR3249870DOI10.1007/s00233-013-9512-9
  11. East, J., 10.1007/s00012-015-0347-y, Algebra Univers. 74 (2015), 207-228. (2015) Zbl1332.20061MR3397434DOI10.1007/s00012-015-0347-y
  12. Fernandes, V. H., 10.1080/00927870008827033, Commun. Algebra 28 (2000), 3401-3426. (2000) Zbl0952.20048MR1765325DOI10.1080/00927870008827033
  13. Fernandes, V. H., Gomes, G. M. S., Jesus, M. M., Presentations for some monoids of injective partial transformations on a finite chain, Southeast Asian Bull. Math. 28 (2004), 903-918. (2004) Zbl1078.20060MR2115137
  14. Fernandes, V. H., Gomes, G. M. S., Jesus, M. M., 10.1081/AGB-200047446, Commun. Algebra 33 (2005), 587-604. (2005) Zbl1072.20079MR2124347DOI10.1081/AGB-200047446
  15. Ganyushkin, O., Mazorchuk, V., 10.1007/978-1-84800-281-4, Algebra and Applications 9, Springer, London (2009). (2009) Zbl1166.20056MR2460611DOI10.1007/978-1-84800-281-4
  16. Ganyushkin, O., Mazorchuk, V., On Kiselman quotients of 0-Hecke monoids, Int. Electron. J. Algebra 10 (2011), 174-191. (2011) Zbl1263.20053MR2821178
  17. Higgins, P. M., 10.1016/S0304-3975(96)00230-7, Theor. Comput. Sci. 178 (1997), 257-264. (1997) Zbl0901.68093MR1453853DOI10.1016/S0304-3975(96)00230-7
  18. Kudryavtseva, G., Mazorchuk, V., 10.2478/s11533-006-0017-6, Cent. Eur. J. Math. 4 (2006), 413-434. (2006) Zbl1130.20041MR2233859DOI10.2478/s11533-006-0017-6
  19. Laradji, A., Umar, A., Combinatorial results for semigroups of order-decreasing partial transformations, J. Integer Seq. 7 (2004), Art. 04.3.8, 14 pages. (2004) Zbl1064.05016MR2110779
  20. Maltcev, V., Topics in Combinatorial Semigroup Theory, Ph.D. Thesis, University of St. Andrews, United Kingdom (2012). (2012) MR3271783
  21. Maltcev, V., Mazorchuk, V., Presentation of the singular part of the Brauer monoid, Math. Bohem. 132 (2007), 297-323. (2007) Zbl1163.20035MR2355660
  22. Mazorchuk, V., Steinberg, B., 10.1007/s10801-011-0336-y, J. Algebr. Comb. 36 (2012), 333-354. (2012) Zbl1259.05190MR2969066DOI10.1007/s10801-011-0336-y
  23. Popova, L. M., Defining relations of a semigroup of partial endomorphisms of a finite linearly ordered set, Leningr. Gos. Ped. Inst. A. I. Gertsen, Uch. Zap. 238 (1962), 78-88 Russian. (1962) Zbl0214.27002MR0177050
  24. Ruškuc, N., 10.1007/BF02573640, Semigroup Forum 51 (1995), 319-333. (1995) Zbl0840.20061MR1351958DOI10.1007/BF02573640
  25. Ruškuc, N., Semigroup Presentations, Ph.D. Thesis, University of St. Andrews, United Kingdom (1995). (1995) 
  26. Solomon, A., 10.1007/BF02574150, Semigroup Forum 53 (1996), 351-368. (1996) Zbl0862.20049MR1406781DOI10.1007/BF02574150
  27. Umar, A., 10.1017/S0308210500015031, Proc. R. Soc. Edinb., Sect. A 120 (1992), 129-142. (1992) Zbl0746.20048MR1149989DOI10.1017/S0308210500015031
  28. Umar, A., Semigroups of Order-Decreasing Transformations, Ph.D. Thesis, University of St. Andrews, United Kingdom (1992). (1992) MR1491911
  29. Umar, A., 10.1017/S0308210500025737, Proc. R. Soc. Edinb., Sect. A 123 (1993), 355-363. (1993) Zbl0789.20075MR1215419DOI10.1017/S0308210500025737
  30. Umar, A., Presentations for subsemigroups of P D n , Available at https://arxiv.org/abs/1702.02788 (2017), 7 pages. (2017) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.