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标题：Maximum and Minimum Works Performed by T˜n
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作者：Pokalas P. Tal ; M. S. Mahmud ; M. A. Mbah 等
期刊名称：Modern Applied Science
印刷版ISSN：1913-1844
电子版ISSN：1913-1852
出版年度：2022
卷号：16
期号：2
页码：23-29
DOI：10.5539/mas.v16n2p23
语种：English
出版社：Canadian Center of Science and Education
摘要：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.
关键词：transformation;full transformation;signed full transformation;work