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Publications Influence

Combinatorial Results for Semigroups of Order-Preserving
Full Transformations

- A. Laradji, A. Umar
- Mathematics
- 12 March 2006

AbstractLet On be the semigroup of all order-preserving full
transformations of a finite chain, say Xn = {1, 2, ..., n}, and for a given full transformation α: Xn → Xn let f(α) = |{x ∈ Xn: xα = x}|.… Expand

30 3

Asymptotic Results for Semigroups of Order-Preserving Partial Transformations

- A. Laradji, A. Umar
- Mathematics
- 1 February 2006

ABSTRACT Let 𝒫 𝒞 n be the semigroup of all decreasing and order-preserving partial transformations of an n-element chain, and let E(𝒫 𝒞 n ) be its set of idempotents. Among other results,… Expand

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Combinatorial results for semigroups of order-preserving partial transformations

- A. Laradji, A. Umar
- Mathematics
- 1 August 2004

Abstract Let PO n be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that | PO n |=c n satisfies the recurrence (2n−1)(n+1)c n+1 =4 3n 2 −1 c n… Expand

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Combinatorial Results for the Symmetric Inverse Semigroup

- A. Laradji, A. Umar
- Mathematics
- 1 September 2007

In this note we obtain and discuss formulae for the number of partial one-one transformations (of an n-element set) of height (equivalently, width) r and having exactly k fixed points. Moreover, we… Expand

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Classroom note: A Generalization of Leibniz rule for higher derivatives

- A. Thaheem, A. Laradji
- Mathematics
- 1 November 2003

This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculus… Expand

8 1

On Certain Finite Semigroups of
Order-decreasing Transformations I

- A. Laradji, A. Umar
- Mathematics
- 18 March 2004

Let $D_n $ (${\cal O}_n$) be the semigroup of all finite order-decreasing (order-preserving) full transformations of an $n$-element chain, and let $D(n,r) = \{\alpha\in D_n: |\mbox{Im}\alpha| \leq… Expand

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On lifts of irreducible 2-Brauer characters of solvable groups

- A. Laradji
- Mathematics
- 1 June 2002

Let be a finite group. Write| | = , where is a prime number and ( ) = 1, and letQ = Q( 2π / ), the field generated by2π / over the fieldQ of rationals. Recall that an ordinary character χ of is said… Expand

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On the Number of Nilpotents in the Partial Symmetric Semigroup

- A. Laradji, A. Umar
- Mathematics
- 31 December 2004

Abstract In this note, we obtain and discuss formulae for the total number of nilpotent partial and nilpotent partial one–one transformations of a finite set.

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Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations

- A. Laradji, A. Umar, K. Fahd
- Mathematics
- 2004

Let PCn be the semigroup of all decreasing and order-preserving partial transformations of a flnite chain. It is shown that jPCnj = rn, where rn is the large (or double)

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Polynomial solutions of differential equations

- H. Azad, A. Laradji, M. Mustafa
- Mathematics, Physics
- 22 February 2010

AbstractA new approach for investigating polynomial solutions of differential equations is proposed. It is based on elementary linear algebra. Any differential operator of the form… Expand

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