Enumeration of Partial Contraction Transformation Semi-groups
1 Department of Mathematics and Computer Science, Faculty of Science, Federal University of Kashere, P.M.B 0182, Gombe, Gombe State
2 Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin
* Corresponding author: sakinwunmi@fukashere.edu.ng
2 Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin
* Corresponding author: sakinwunmi@fukashere.edu.ng
Abstract
Let M = {1, 2 . . . n} on a partial transformation α,
dom (α) : |αx − αy| whenever x, y ∈ dom(α) and |x − y|,
then the semi-group CP T(M) of all contraction partial
transformation of M is denoted by CP T n. In this article, we derive the formula for some of the (sequences)
values of CP T n and obtained that |P Cn| =
Pn
k=0
n−2
q−3
,
|P ODn| =
n−(p−1)
n−p
and |αS| = 2n − 1 = 3n + 3.
Keywords
Contraction mapping
Collapse
Height
Waist
Semi-group
How to Cite
Akinwunmi, S. A., & Makanjuola, S. O. (2019). Enumeration of Partial Contraction Transformation Semi-groups. Nigerian Journal of Mathematics and Applications, 29(2), 70-77. https://doi.org/10.67897/njma.2019.non1bmd6
S. A. Akinwunmi, and S. O. Makanjuola, "Enumeration of Partial Contraction Transformation Semi-groups," Nigerian Journal of Mathematics and Applications, vol. 29, no. 2, pp. 70-77, December 2019. doi: 10.67897/njma.2019.non1bmd6
