Browsing by Author "Kamuti, Ireri"

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    Cycle Index Formulas for D n Acting on Unordered Pairs
    (Uoem, 2015) Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; Kimani, Patrick Mwangi
    The cycle index of dihedral group D n acting on the set of X the vertices of a regular n- gon was studied (See [1]). In this paper we study the cycle index formulas of D n acting on unordered pairs from the set . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of and an odd value of .1.
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    Cycle Index Formulas for Dn Acting on Ordered pairs
    (UoEm, 2016-04) Muthoka, Geoffrey; Kamuti, Ireri; Kimani, Patrick; Hussein, Lao
    The cycle index of dihedral group Dn acting on the set of the vertices of a regular n-gon was studied by Harary and Palmer in 1973 [1]. Since then a number of researchers have studied the cycle indices dihedral group acting on different sets X={1,2,...,n} and the resulting formulas Dn have found applications in enumeration of a number of items. Muthoka (2015) [2] studied the cycle index formula of the –the n vertices of a regular -gon. In this paper we study the dihedral group acting on unordered pairs from the set X={1,2,..,n} cycle index formulas of acting on ordered pairs from the set . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of and an odd value of n .
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    Cycle Index Formulas for Dn Acting on Unordered Pairs
    (UoEm, 2015) Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; kimani, patrick
    The cycle index of dihedral group Dn acting on the set X of the vertices of a regular -gon was studied (See [1]). In this paper we study the cycle index formulas of Dn acting on unordered pairs from the set x . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of n and an odd value of n .
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    Rank and Subdegrees of P GL(2, q) Acting Cosets of P GL(2, e) for q an Even Power of e
    (UoEm, 2019) Kimani, Patrick; Kamuti, Ireri; Rimberia, Jane
    The action of projective general group on the cosets of its maximal subgroups has been studied. For instance, [9] studied the action of G on the cosets of P GL(2, e) when q is an odd prime power of e. In this paper, we determine the rank and subdegrees of the action of P GL(2, q) on the cosets of its subgroup P GL(2, e) for odd q and an even power of e. We apply the table of marks to achieve this.
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    Rank and Subdegrees of PGL(2; q) Acting Cosets of PGL(2; e) for q an Even Power of e
    (UoEm, 2019) Kimani, Patrick Mwangi; Kamuti, Ireri; Rimberia, Jane
    The action of projective general group on the cosets of its maximal subgroups has been studied. For instance, [9] studied the action of G on the cosets of PGL(2; e) when q is an odd prime power of e. In this paper, we determine the rank and subdegrees of the action of PGL(2; q) on the cosets of its subgroup PGL(2; e) for odd q and an even power of e. We apply the table of marks to achieve this.
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    Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups
    (UoEm, 2020) Agwanda, Siahi Maxwell; Kimani, Patrick; Kamuti, Ireri
    The action of affine groups on Galois field has been studied. For instance, [3] studied the action of 𝐴𝑓𝑓 (𝑞 ) on Galois field 𝐺𝐹 (𝑞) for 𝑞 a power of prime 𝑝. In this paper, the rank and subdegree of the direct product of affine groups over Galois field acting on the cartesian product of Galois field is determined. The application of the definition of the product action is used to achieve this. The ranks and subdegrees are used in determination of suborbital graph, the non-trivial suborbital graphs that correspond to this action have been constructed using Sims procedure and were found to have a girth of 0, 3, 4 and