Defect theorems with compatibility relations

We consider words together with a compatibility relation induced by a relation on letters. Unique factorization with respect to two arbitrary word relations R and S defines the ( R , S )-freeness of the semigroup considered. We generalize the stability theorem of Schützenberger and Tilson’s closure...

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Bibliographic Details
Published in:Semigroup forum 2008, Vol.76 (1), p.1-24
Main Authors: Halava, Vesa, Harju, Tero, Kärki, Tomi
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Research Article
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Summary:We consider words together with a compatibility relation induced by a relation on letters. Unique factorization with respect to two arbitrary word relations R and S defines the ( R , S )-freeness of the semigroup considered. We generalize the stability theorem of Schützenberger and Tilson’s closure result for ( R , S )-free semigroups. The inner and the outer ( R , S )-unique factorization hull and the ( R , S )-free hull of a set of words are introduced and we show how they can be computed. We prove that the ( R , S )-unique factorization hulls possess a defect effect, which implies a variant of a cumulative defect theorem of word semigroups. In addition, a defect theorem of partial words is proved as a corollary.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-007-9013-9