Cycle Indices of Cyclic and Dihedral Groups Acting on Diagonals of a Regular N-Gon and R-Element Subsets of the Set X = * +.

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dc.contributor.advisorIreri. N. Kamutien_US
dc.contributor.authorPaul, Doris Kiende
dc.date.accessioned2022-09-27T07:42:55Z
dc.date.available2022-09-27T07:42:55Z
dc.date.issued2022
dc.descriptionA Research Project Submitted in Partial and fulfillment of the Requirements for the Award of the Degree of Master of Science (Pure Mathematics) in the School of Pure and Applied Sciences of Kenyatta University, March, 2022en_US
dc.description.abstractPolya (1937) used the cycle index in counting configurations. Several authors have computed cycle index formula of several group actions which have been used globally in chemistry and mathematics, in counting of chemical compounds and graphs. However dihedral group Dn acting on the set of diagonals of a regular n - gon, 4-elements and r-elements subsets of the set X = ( 1,2,…n) has not been done. The project shall come up with the formulae for Z. / and Z. /= [Σ ( ) ]. The project seek to extend Muthoka’s findings on the formula for Z( , -) and Z( , -) to derive the formulae for Z( , -) and Z( , -) = [Σ ( ) ( ) ( ) . ( ) ( )/]. This shall be done by re-visiting some of the results by Harary and Palmer (1973) and also some of the contributions by Kamuti and Njuguna (2004) in the study shall be used.en_US
dc.description.sponsorshipKenyatta Universityen_US
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/24292
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectCycle Indicesen_US
dc.subjectCyclicen_US
dc.subjectDihedral Groupsen_US
dc.subjectDiagonalsen_US
dc.subjectRegular N-Gonen_US
dc.subjectR-Element Subsetsen_US
dc.subjectSet X = * +.en_US
dc.titleCycle Indices of Cyclic and Dihedral Groups Acting on Diagonals of a Regular N-Gon and R-Element Subsets of the Set X = * +.en_US
dc.typeThesisen_US
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