Density of Metric Small Cancellation in Finitely Presented Groups

Bishop, A; Ferov, M

Density of Metric Small Cancellation in Finitely Presented Groups

Bishop, A

Ferov, M

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Publisher:: Episciences.org
Publication Type:: Journal Article
Citation:: Groups, Complexity, Cryptology, 2020, 12, (2), pp. 1-18
Issue Date:: 2020-02-18

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Field	Value	Language
dc.contributor.author	Bishop, A https://orcid.org/0000-0001-6803-1143
dc.contributor.author	Ferov, M
dc.date.accessioned	2022-10-31T03:29:24Z
dc.date.available	2022-10-31T03:29:24Z
dc.date.issued	2020-02-18
dc.identifier.citation	Groups, Complexity, Cryptology, 2020, 12, (2), pp. 1-18
dc.identifier.issn	1867-1144
dc.identifier.issn	1869-6104
dc.identifier.uri	http://hdl.handle.net/10453/163044
dc.description.abstract	Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information about "small" group presentations. In this note, we give closed-form formulas for both lower and upper bounds on the density of small cancellation presentations, and compare our results with experimental data.
dc.language	en
dc.publisher	Episciences.org
dc.relation.ispartof	Groups, Complexity, Cryptology
dc.relation.isbasedon	10.46298/jgcc.2020.12.2.6200
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	08 Information and Computing Sciences
dc.title	Density of Metric Small Cancellation in Finitely Presented Groups
dc.type	Journal Article
utslib.citation.volume	12
utslib.for	08 Information and Computing Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access	*
pubs.consider-herdc	false
dc.date.updated	2022-10-31T03:29:23Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	12
utslib.citation.issue	2

Abstract:

Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information about "small" group presentations. In this note, we give closed-form formulas for both lower and upper bounds on the density of small cancellation presentations, and compare our results with experimental data.

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http://hdl.handle.net/10453/163044