Maximum and Minimum Works Performed by TËœn

Pokalas P. Tal, M. S. Mahmud, M. A. Mbah and R. U. Ndubuisi

Modern Applied Science, 2022, vol. 16, issue 2, 23

Abstract: Let Xn and X*n be the finite sets {1,2,3,...,n} and {±1,±2,±3,..,±n} respectively. A map α- Xn→Xn is called a transformation on Xn We call α a signed transformation if α- Xn→X*n Let Tn and T˜n be the sets of full and signed full transformations on Xn respectively. The work, w(α) performed by a transformation α is defined as the sum of all the distances |i-iα| for each i ϵ dom(α) In this paper, we present a range for the values of w(α) for all α ϵ Tn. Further, we characterize elements of T˜n that attain minimum and maximum works and provide formulas for the values of these minimum and maximum.

Date: 2022
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