Cycle Index of Internal Direct Product Groups
| dc.contributor.author | Kamuti, I.N. | |
| dc.date.accessioned | 2013-12-17T08:56:05Z | |
| dc.date.available | 2013-12-17T08:56:05Z | |
| dc.date.issued | 2011-12 | |
| dc.description.abstract | If M and H are permutation groups with cycle indices ZM and ZH respectively, and if * is some binary operation on permutation groups, then a fundamental problem in enumerative combinatorics is the determination of a formula for ZM *H in terms of ZM and ZH. To this end, a number of results have already been obtained (cf. Harary [1], [2], [3]; Harary and Palmer [6]; Harrison and High [7]; Pόlya [10]). This paper may be viewed as a continuation of a previous paper (Kamuti [8]) in which I have shown how the cycle index of a semidirect product group G= M×H can be expressed in terms of the cycle indices of M and H by considering semidirect products called Frobenius groups. Thus if G=M×H (internal direct product), the aim of this paper is to express the cycle index of G in terms of the cycle indices of M and H when G acts on the cosets of H in G. | en_US |
| dc.identifier.citation | International Mathematical F orum, Vol. 7, 2012, no. 30, 1491 - 1494 | en_US |
| dc.identifier.uri | http://ir-library.ku.ac.ke/handle/123456789/8076 | |
| dc.language.iso | en | en_US |
| dc.publisher | International Mathematical Forum | en_US |
| dc.subject | Internal direct product | en_US |
| dc.subject | Equivalent actions | en_US |
| dc.subject | Cycle indices | en_US |
| dc.title | Cycle Index of Internal Direct Product Groups | en_US |
| dc.type | Article | en_US |