AVERAGE AND EXTREMAL VALUES OF COMPLETE WORK-DONE ON TRANSFORMATION SEMIGROUPS

Gabriel Frank; Folake L. Joseph; Emmanuel O. Ohwadua

doi:10.5281/zenodo.20999895

Gabriel Frank Bingham University, Karu, Nasarawa State, Nigeria
Folake L. Joseph Bingham University, Karu, Nasarawa State, Nigeria
Emmanuel O. Ohwadua Bingham University, Karu, Nasarawa State, Nigeria

DOI: https://doi.org/10.5281/zenodo.20999895

Abstract

In this paper, we study a complete work-done function defined on three important transformation semigroups: the full transformation semigroup (T_n), the partial transformation semigroup (P_n), and the symmetric inverse semigroup (I_n). For each class, closed formulae are obtained for the total and average values of the complete work-done function. Extremal values are also determined for (T_n) and (P_n). The results show that algebraic restrictions such as partiality and injectivity significantly influence the magnitude and distribution of the complete work-done values. Numerical tables and graphical illustrations are provided for
1 ≤ n ≤ 10 to support the theoretical findings.

MSC (2020): Primary 05A15, Secondary 20M10, 20M20

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