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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2356-6140 1537-744X |