참고문헌
- G. Ayik, H. Ayik, L. Bugay, and O. Kelekci, Generating sets of finite singular transformation semigroups, Semigroup Forum 86 (2013), no. 1, 59-66. https://doi.org/10.1007/s00233-012-9379-1
- G. Ayik, H. Ayik, and M. Koc, Combinatorial results for order-preserving and order-decreasing transformations, Turkish J. Math. 35 (2011), no. 4, 617-625.
- O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups, Springer-Verlag, London, 2009.
- G. U. Garba, On the idempotent ranks of certain semigroups of order-preserving transformations, Portugal. Math. 51 (1994), no. 2, 185-204.
- G. M. S. Gomes and J. M. Howie, On the ranks of certain semigroups of order-preserving transformations, Semigroup Forum 45 (1992), no. 3, 272-282. https://doi.org/10.1007/BF03025769
- P. M. Higgins, The product of the idempotents and an H-class of the finite full transformation semigroup, Semigroup Forum 84 (2012), no. 2, 203-215. https://doi.org/10.1007/s00233-012-9373-7
- J. M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, New York, 1995.
- S. Sornsanam and R. P. Sullivan, Regularity conditions on order-preserving transformation semigroups, Southeast Asian Bull. Math. 28 (2004), 333-342.
- R. J. Wilson and J. J. Watkins, Graphs: An Introductory Approach, Wiley, 1990.
- H. Yang and X. Yang, Automorphisms of partition order-decreasing transformation monoids, Semigroup Forum 85 (2012), no. 3, 513-524. https://doi.org/10.1007/s00233-012-9430-2
- P. Zhao, B. Xu, and M. Yang, A Note on maximal properties of some subsemigroups of finite order-preserving transformation semigroups, Comm. Algebra 40 (2012), no. 3, 1116-1121. https://doi.org/10.1080/00927872.2010.546002