Browsing by Author "Bakare, G. N.,"

Now showing 1 - 5 of 5
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    Conjugacy classes of the order-preserving and order-decreasing partial one-to-one transformation semigroups
    (Journal of Science, Technology, Mathematics and Education. Published by the Department of Science Education, Federal University of Technology, Minna, Nigeria., 2019-03) Ugbene, I. J.,; Bakare, G. N.,; Ibrahim G. R.
    In this paper I_n is considered to be the partial one-to-one transformation semigroup on . The order-preserving and order-decreasing partial one-to-one transformation semigroup(〖IC〗_n) is defined to be the subsemigroups of I_n. The nilpotent and idempotent elements of 〖IC〗_n were then obtained from its conjugacy classes using path structure to be n+1 and 1/192 n^4-1/16 n^3+29/48 n^2-n+2 respectively. The index and period of each conjugacy classes were also found. More so, some properties of conjugacy classes were stated.
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    Further Results on Combinatorial Properties of Order-Preserving Alternating Semigroups.
    (Confluence Journal of Pure and Applied Sciences. Published by Faculty of Science, Federal University Lokoja, Kogi State, Nigeria., 2018-11) Bakare, G. N.,; Makanjuola, S. O.
    Let Cn be the charts on Xn = {1,2,...,n} be the alternating semigroups, OAnc be the subsemigroups of order preserving alternating semigroups and N(S) be the set of nilpotents element of a semigroups OAnc . Let G(n;p,m) = | {aeS : h(a) = p^f(a) = m }| ,G(n;m) = | {aeS : f(a) = m }| and G(p; m) = | {aeS : h(a) = p }| . In this paper, some combinatorial properties of OAnc for two parameters G(n; p) were discuss and their nilpotent elements were also investigated.
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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.
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    Some Results on Properties of Alternating Semigroups.
    (Nigerian Journal of Mathematics and Applications. Published by Mathematical Association of Nigeria., 2015) Bakare, G. N.,; Makanjuola, S. O.
    Let Cn be the symmetric inverse semigroup on Xn = {1,2,...,n}, Anc be the alternating semigroups of Xn. In this paper, we discuss some combinatorial properties in Anc and obtained some triangle of numbers for it.
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    Tropicalization of Idempotent Elements on Full Transformation Semigroup.
    (Confluence Journal of Pure and Applied Sciences. Published by Faculty of Science, Federal University Lokoja, Kogi State Nigeria., 2018-06) Usamot, I. F.,; Bakare, G. N.,; Ahmed, B. M.
    This paper consists of exposition for tropical geometry and its applications on Idempotent elements in Semigroup of Full Transformation E(Tn) . We started the exposition with classical algebra into tropical algebra and shown how tropical curves degenerate tropical polynomial in E(Tn).