Browsing by Author "Makanjuola"

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    On the number of order-preserving alternating semigroups
    (Journal of Nigerian Association of Mathematical Physics. Published by Nigerian Association of Mathematical Physics., 2014-11) Bakare, G. N.,; Ibrahim, S.O.; Makanjuola
    A semigroup is an algebraic structure consisting of a non-empty set S together with an associative binary operation. A transformation on X is a function from X to itself. Transformation semigroups are one of the most fundamental mathematical objects. They occur in theoretical computer science, where properties of language depend on algebraic properties of various transformation semigroups related to them. Let Cn the symmetricinverse semigroup on Xn = {1,2,3,…,,n}, Anc be the alternating semigroups on n-0bject and OAnc be its subsemigroup of order preserving alternating semigroup of Xn. The set E(OAnc) and N(OAnc) be its idempotent and nilpotent elements of order preserving alternating semigroups of Xn. In this paper, we obtain and discuss formulae for the number of E(OAnc) and N(OAcn) respectively. We also characterize the Green relation on OAcn.