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[w...

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Detalles Bibliográficos
Autores principales: Mushtaq, Qaiser, Razaq, Abdul
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4170709/
https://www.ncbi.nlm.nih.gov/pubmed/25333072
http://dx.doi.org/10.1155/2014/505496
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author Mushtaq, Qaiser
Razaq, Abdul
author_facet Mushtaq, Qaiser
Razaq, Abdul
author_sort Mushtaq, Qaiser
collection PubMed
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[w (i), w (j)] such that both w (i) and w (j) 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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spelling pubmed-41707092014-10-20 Equivalent Pairs of Words and Points of Connection Mushtaq, Qaiser Razaq, Abdul ScientificWorldJournal Research Article 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[w (i), w (j)] such that both w (i) and w (j) 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. Hindawi Publishing Corporation 2014 2014-09-08 /pmc/articles/PMC4170709/ /pubmed/25333072 http://dx.doi.org/10.1155/2014/505496 Text en Copyright © 2014 Q. Mushtaq and A. Razaq. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Mushtaq, Qaiser
Razaq, Abdul
Equivalent Pairs of Words and Points of Connection
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
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4170709/
https://www.ncbi.nlm.nih.gov/pubmed/25333072
http://dx.doi.org/10.1155/2014/505496
work_keys_str_mv AT mushtaqqaiser equivalentpairsofwordsandpointsofconnection
AT razaqabdul equivalentpairsofwordsandpointsofconnection

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