On the defect theorem and simpliflability.
On the deficit of a set of words.
On the degree of finite maximal biprefix codes.
On the Delta set of a singular arithmetical congruence monoid
If and are positive integers with and , then the setis a multiplicative monoid known as an arithmetical congruence monoid (or ACM). For any monoid with units and any we say that is a factorization length of if and only if there exist irreducible elements of and . Let be the set of all such lengths (where whenever ). The Delta-set of the element is defined as the set of gaps in : and the Delta-set of the monoid is given by . We consider the when is an ACM with...
On the equality sets for homomorphisms on free monoids with two generators
On the finite basis property for semigroup varieties.
On the Frobenius number of some Lucas numerical semigroups.
On the fundamental double four-spiral semigroup.
On the graph labellings arising from phylogenetics
We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
On the idempotent ranks of certain semigroups of order-preserving transformations.
On the invariance of small overlap hypotheses.
On the inverse braid and reflection monoids of type .
On the maximal subsemigroups of the semigroup of all monotone transformations
In this paper we consider the semigroup Mₙ of all monotone transformations on the chain Xₙ under the operation of composition of transformations. First we give a presentation of the semigroup Mₙ and some propositions connected with its structure. Also, we give a description and some properties of the class of all monotone transformations with rank n-1. After that we characterize the maximal subsemigroups of the semigroup Mₙ and the subsemigroups of Mₙ which are maximal in .
On the membership problem for pseudo-varieties of commutative semigroups.
On the nilpotent rank of partial transformation semigroups.
On the periodicity of morphisms on free monoids
On the ranks of certain finite semigroups of order-decreasing transformations.
On the ranks of certain semigroups of order-preserving transformations.
On the representation of abstract semigroups by transformation semigroups : Computer investigations.
On the saturated numerical semigroups
In this study, we characterize all families of saturated numerical semigroups with multiplicity four. We also present some results about invariants of these semigroups.