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Defect Theorems with Compatibility Relation

Vesa Halava, Tero Harju, Tomi Kärki, Defect Theorems with Compatibility Relation. Semigroup Forum 76, 1–24, 2008.

Abstract:

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.

BibTeX entry:

@ARTICLE{jHaHaKa08a,
  title = {Defect Theorems with Compatibility Relation},
  author = {Halava, Vesa and Harju, Tero and Kärki, Tomi},
  journal = {Semigroup Forum},
  volume = {76},
  pages = {1–24},
  year = {2008},
  keywords = {unique factorization, free semigroup, stability, compatibility relation, defect theorem, partial word},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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