Equivalent Pairs of Words and Points of Connection
Higman has defined coset diagrams for PGL(2,Z). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in Z[z], obtained by choosing a pair of words F[wi,...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/505496 |
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| _version_ | 1832545834592370688 |
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| author | Qaiser Mushtaq Abdul Razaq |
| author_facet | Qaiser Mushtaq Abdul Razaq |
| author_sort | Qaiser Mushtaq |
| collection | DOAJ |
| description | Higman has defined coset diagrams for PGL(2,Z). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in Z[z], obtained by choosing a pair of words F[wi,wj] such that both wi and wj fix a vertex v in γ. Two pairs of words are equivalent if and only if they have the same polynomial. In this paper, we find distinct pairs of words that are equivalent. We also show there are certain fragments, which have the same orientations as those of their mirror images. |
| format | Article |
| id | doaj-art-1c8e94a250114a048fd1cd462182a52a |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-1c8e94a250114a048fd1cd462182a52a2025-02-03T07:24:31ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/505496505496Equivalent Pairs of Words and Points of ConnectionQaiser Mushtaq0Abdul Razaq1Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanDepartment of Mathematics, Quaid-i-Azam University, Islamabad, PakistanHigman has defined coset diagrams for PGL(2,Z). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in Z[z], obtained by choosing a pair of words F[wi,wj] such that both wi and wj fix a vertex v in γ. Two pairs of words are equivalent if and only if they have the same polynomial. In this paper, we find distinct pairs of words that are equivalent. We also show there are certain fragments, which have the same orientations as those of their mirror images.http://dx.doi.org/10.1155/2014/505496 |
| spellingShingle | Qaiser Mushtaq Abdul Razaq Equivalent Pairs of Words and Points of Connection The Scientific World Journal |
| title | Equivalent Pairs of Words and Points of Connection |
| title_full | Equivalent Pairs of Words and Points of Connection |
| title_fullStr | Equivalent Pairs of Words and Points of Connection |
| title_full_unstemmed | Equivalent Pairs of Words and Points of Connection |
| title_short | Equivalent Pairs of Words and Points of Connection |
| title_sort | equivalent pairs of words and points of connection |
| url | http://dx.doi.org/10.1155/2014/505496 |
| work_keys_str_mv | AT qaisermushtaq equivalentpairsofwordsandpointsofconnection AT abdulrazaq equivalentpairsofwordsandpointsofconnection |