String rewriting for Double Coset Systems

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dc.creatorBrown, Ronald
dc.creatorGhani, Neil
dc.creatorHeyworth, Anne
dc.creatorWensley, Christopher D.
dc.date2005-08-21
dc.date.accessioned2026-07-07T05:22:32Z
dc.date.available2026-07-07T05:22:32Z
dc.descriptionIn this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not suffer this restriction and we present some examples of infinite double coset systems which can now easily be solved using our approach. Even when both enumerative and rewriting techniques are present, our rewriting methods will be competitive because they i) do not require the preliminary calculation of cosets; and ii) as with single coset problems, there are many examples for which rewriting is more effective than enumeration. Automata provide the means for identifying expressions for normal forms in infinite situations and we show how they may be constructed in this setting. Further, related results on logged string rewriting for monoid presentations are exploited to show how witnesses for the computations can be provided and how information about the subgroups and the relations between them can be extracted. Finally, we discuss how the double coset problem is a special case of the problem of computing induced actions of categories which demonstrates that our rewriting methods are applicable to a much wider class of problems than just the double coset problem.
dc.descriptionaccepted for publication by the Journal of Symbolic Computation
dc.identifierhttps://arxiv.org/abs/math/0508391
dc.identifierhttp://arxiv.org/abs/math/0508391
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76098
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject20F05; 20F10
dc.titleString rewriting for Double Coset Systems
dc.typetext

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