The inverse hull of the free semigroup on a set X.
The local and global varieties induced by nilpotent monoids
The local catenativity of DOL-sequences in free commutative monoids is decidable in the binary case
The minimal right -ideal of the free semigroup on a countable set
The monoid of ordered partitions of a natural number.
The monoid of suspensions and loops modulo Bousfield equivalence
The suspension and loop space functors, Σ and Ω, operate on the lattice of Bousfield classes of (sufficiently highly connected) topological spaces, and therefore generate a submonoid ℒ of the complete set of operations on the Bousfield lattice. We determine the structure of ℒ in terms of a single parameter of homotopy theory which is closely tied to the problem of desuspending weak cellular inequalities.
The one-block property in varieties of semigroups.
The proof of Birman's conjecture on singular braid monoids.
The rank of a commutative semigroup
The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups by defining as the supremum of cardinalities of finite independent subsets of . Representing such a semigroup as a semilattice of (archimedean) components , we prove that is the supremum of ranks of various . Representing a commutative separative semigroup as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations...
The topology of the free topological semigroup
The word problem for nilpotent inverse monoids.
The word problem in regular band free products.
There are ternary circular square-free words of length for 18.
Topologie -adique sur les mots
Cet article est une introduction aux aspects combinatoires de la distance -adique et de la topologie -adique sur les mots. On donne plusieurs définitions équivalentes de ces notions, illustrées par divers exemples et propriétés. Après avoir décrit de façon détaillée les ouverts, on démontre que la distance -adique est uniformément équivalente à une distance obtenue à partir des coefficients binomiaux définis sur les mots. On donne également deux exemples de suites convergentes dans la topologie...
Towards parametrizing word equations
Classically, in order to resolve an equation over a free monoid , we reduce it by a suitable family of substitutions to a family of equations , , each involving less variables than , and then combine solutions of into solutions of . The problem is to get in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to . We carry out such a parametrization in the case the prime equations in the graph...
Towards parametrizing word equations
Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family of substitutions to a family of equations uf ≈ vf, , each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the...
Trees, band monoids, and formal languages.
Trees in commtative nil-semigroups of index two