The dual braid monoid
David Bessis (2003)
Annales scientifiques de l'École Normale Supérieure
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David Bessis (2003)
Annales scientifiques de l'École Normale Supérieure
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V. V. Vershinin (2014)
Banach Center Publications
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In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation for generalizations of braids. Namely, we consider presentations with small number of generators, Sergiescu graph-presentations and Birman-Ko-Lee presentation. The work of V.~V.~Chaynikov on the word and conjugacy problems for the...
Alfred Geroldinger (1998)
Colloquium Mathematicae
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Arkowitz, Martin, Gutierrez, Mauricio (1997)
International Journal of Mathematics and Mathematical Sciences
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Víctor Blanco, Pedro A. García-Sánchez, Alfred Geroldinger (2010)
Actes des rencontres du CIRM
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Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.
Fountain, John, Gomes, Gracinda M.S. (1994)
Portugaliae Mathematica
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A. Geroldinger, F. Halter-Koch (1994)
Semigroup forum
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U. Knauer, A. Mikhalev (1980)
Semigroup forum
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L. Skornjakov (1982)
Banach Center Publications
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Scott T. Chapman, Felix Gotti, Roberto Pelayo (2014)
Colloquium Mathematicae
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Let M be a commutative cancellative monoid. The set Δ(M), which consists of all positive integers which are distances between consecutive factorization lengths of elements in M, is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with cyclic class group of order n ≥ 3, then it is well-known that Δ(M) ⊆ {1,..., n-2}. Moreover, equality holds for this containment when each class contains a prime divisor from M. In this note, we consider the question...