References

ON THE SEMIGROUP OF ORDER-DECREASING PARTIAL ISOMETRIES OF A FINITE CHAIN


[1] F. Al Kharousi, R. Kehinde and A. Umar, On the semigroup of partial isometries of a finite chain, Comm. Algebra 44(2) (2016), 639-647.
DOI: https://doi.org/10.1080/00927872.2014.984838

[2] F. Al Kharousi, R. Kehinde and A. Umar, Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain (Submitted).

[3] D. Borwein, S. Rankin and L. Renner, Enumeration of injective partial transformations, Discrete Math. 73(3) (1989), 291-296.
DOI: https://doi.org/10.1016/0012-365X(89)90272-0

[4] L. Bracci and L. E. Picasso, Representations of semigroups of partial isometries, Bull. Lond. Math. Soc. 39(5) (2007), 792-802.
DOI: https://doi.org/10.1112/blms/bdm059

[5] J. Doyen, Equipotence et unicité de systèmes generateurs minimaux dans certains monoides, Semigroup Forum 28(1) (1984), 341-346.
DOI: https://doi.org/10.1007/BF02572494

[6] A. El-Qallali and J. B. Fountain, Idempotent-connected abundant semigroups, Proc. Roy. Soc. Edinburgh Sect. A: Math. 91(1-2) (1981), 79-90.
DOI: https://doi.org/10.1017/S0308210500012646

[7] V. H. Fernandes, The monoid of all injective orientation-preserving partial transformations on a finite chain, Comm. Algebra 28(7) (2000), 3401-3426.
DOI: https://doi.org/10.1080/00927870008827033

[8] J. B. Fountain, Adequate semigroups, Proc. Edinburgh Math. Soc. 22(2) (1979), 113-125.
DOI: https://doi.org/10.1017/S0013091500016230

[9] J. B. Fountain, Abundant semigroups, Proc. London Math. Soc. 44(1) (1982), 103-129.
DOI: https://doi.org/10.1112/plms/s3-44.1.103

[10] O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups: An Introduction, Springer-Verlag, London, 2009.

[11] G. U. Garba, Nilpotents in semigroups of partial one-to-one order-preserving mappings, Semigroup Forum 48(1) (1994), 37-49.
DOI: https://doi.org/10.1007/BF02573652

[12] G. M. S. Gomes and J. M. Howie, A P-theorem for inverse semigroups with zero, Portugal. Math. 53(3) (1996), 257-278.

[13] V. Gould, Graph expansions of right cancellative monoids, Internat. J. Algebra Comput. 6(6) (1996), 713-733.
DOI: https://doi.org/10.1142/S0218196796000404

[14] J. M. Howie, Fundamentals of semigroup theory, London Mathematical Society Monographs, New Series 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.

[15] M. V. Lawson, Inverse semigroups, The theory of partial symmetries, World Scientific Publishing Co., Inc., River Edge, NJ, 1998.

[16] M. V. Lawson, The structure of 0-E-unitary inverse semigroups I: The monoid case, Proc. Edinburgh Math. Soc. 42(3) (1999), 497-520.
DOI: https://doi.org/10.1017/S0013091500020484

[17] S. Lipscomb, Symmetric inverse semigroups mathematical surveys and monographs, 46, Amer. Math. Soc., Providence, R.I., 1996.

[18] A. Umar, On the semigroups of partial one-to-one order-decreasing finite transformations, Proc. Roy. Soc. Edinburgh, Sect. A: Math. 123(2) (1993), 355-363.
DOI: https://doi.org/10.1017/S0308210500025737

[19] A. Umar, On certain infinite semigroups of order-increasing transformations II, Arab. J. Sci. Eng. 28(2A) (2003), 203-210.

[20] Lawrence J. Wallen, Semigroups of partial isometries, Bull. Amer. Math. Soc. 75(4) (1969), 763-764.
DOI: https://doi.org/10.1090/S0002-9904-1969-12278-0