The Numerical Work Done by Transformations on a Symmetric Group

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Year:
2020
Type of Publication:
Article
Keywords:
Bijections, Total Work Done, Average Work Done, Power, Partial Transformation
Authors:
Rotimi Kehinde; D. I. Lanlege; A. I. Ma’ali; Abdulrahman Abdulganiyu; Abdulazeez O. Habib
Journal:
IJISM
Volume:
8
Number:
5
Pages:
252-258
Month:
September
ISSN:
2347-9051
Abstract:
The symmetric group of degree n (n is fixed) on a set is the group consisting of all bijections of the set (that is, all one-to-one and onto functions) from the set n = {1, 2, 3,…,n} to itself with function composition as the groups’ operation. In this research, we have mainly presented the total work done, the average work done as well as the power of the transformations on the symmetric group of degree n by assuming elements of n to be set of points that are equally spaced on a line. We have used an effective methodology to generate and generalize formulas for calculating the total work done, the average work done and the power of the transformation by elements of the symmetric group. Results show that there is a huge amount of work done in moving elements of the domain to the elements of the co-domain of the fixed set. We also computed for small values of n the total work done, the average work done by elements of the symmetric group of transformation and the solutions obtained are illustrated graphically. This research work has an important application in physics and theoretical computer science.

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