Orbits in finite semigroups of order preserving transformations
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Abstract (EN)
Let On and Cn be the semigroup of all order-preserving transformations andof all order-preserving and order-decreasing transformations on the finite set Xn =f1;2; : : : ;ng, respectively. Let fix(a) = fx 2 Xn : xa = xg for any transformation a. Inthis thesis, for any Y Xn, we find the cardinalities of the setsOn;Y = fa 2 On : fix(a) =YgandCn;Y = fa 2 Cn : fix(a) =Yg:Moreover, we find the numbers of transformations of On and Cn with r fixed points.Key Words: Transformation semigroups, partial transformation, orderpreserving,orbit,fixed point.
Author
Metin Koç
How to Cite
Metin Koç (Doctorate thesis). Orbits in finite semigroups of order preserving transformations, 2010, Çukurova University.
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