[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