Browsing by Author "Ibrahim, G. R"

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    Characterization of Signed Symmetric Group in Inner Product Spaces
    (Adamawa State University, 2019) Usamot, IF;; Rauf, K;; Bakare, GN;; Ibrahim, G. R
    This paper provides some characterizations of signed symmetric group (SSn) using the notion of orthogonality in inner product spaces. The concepts of ortho-stochastic and reflection were introduced on SSn and results were established with some examples.
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    Combinatorics Properties of Order-preserving Full Contraction Transformation Semigroup by Their Equivalence Classes
    (Department of Mathematics and Statistics, University of Victoria, Canada., 2013) Ibrahim, G. R; Makanjuola, S. O
    In this paper the cardinalities of equivalence classes of starred Green’s relations in order-preserving full contraction transformation semigroup of a finite set(OCT) and the elements in each equivalence classes were investigated. For each class tables were formed, elements were arrange based on their kernel and image sets, patterns of arrangement observed and formulae were deduced in each case through the combinatorial principles.
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    Some characterizations of equivalence relation on contraction mappings
    (Elsevier, 2020) Akinwunmi, S. A;; Mogbonju, M. M;; Ibrahim, G. R
    Let T n be the set of full transformations and P n be the set of partial transformations. It is shown that T n form a semi-group of order n n and P n form a semi-group of order (n+ 1) n. Let ρ (n, m) be a binary relation then we define the image set of ρ (n, m), I (ρ):{n| n∈ N a n d t h e r e e x i s t s m∈ M:(m, n)∈ ρ} whenever (≡ ρ):≡ ρ on a set M is called an equivalence relation if≡ ρ is reflexive, symmetric and transitive. Then, For all m∈ M, we let [m] equivalence class denote the set [m]={n∈ M| n≡ ρ m} with respect to≡ ρ determine by m. Furthermore, we show that D= L∘ R= R∘ L= L υ R implies L⊆ J and R⊆ J. Therefore, D is the minimum equivalence relation class containing L and R. Hence, D⊆ J. If n∈ X m:{n∈ X m| n x n= n; n x= x n} then n∈ D c l a s s is regular. We also show that for L c l a s s, R c l a s s and H c l a s s for all m, n∈ D (α) we have α such that D (α)⊆ M implies I (α)⊆ M. Then for any transformation of …