Related papers: Families of linear semigroups with intermediate gr…
In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
In this paper, we carry out a fairly comprehensive study of two special classes of numerical semigroups, one generated by the sequence of partial sums of an arithmetic progression and the other one generated by the partial sums of a…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
A numerical semigroup is an additive submonoid of the natural numbers with finite complement. The size of the complement is called the genus of the semigroup. How many numerical semigroups have genus equal to $g$? We outline Zhai's proof of…
In this study we introduce the notions of semi-homotopy of semi-continuous maps and of semi-paths. We also construct a group structure, which will be called semi-fundamental group, using semi-loops and explore some properties of…
Here we prove that for dilatation structures linearity (see arXiv:0705.1440v1) is equivalent to a statement about the inverse semigroup generated by the family of dilatations of the space. The result is new for Carnot groups and the proof…
Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…
Some constructions and bounds on the sizes of semiovals contained in the Hermitian curve are given. A construction of an infinite family of 2-blocking sets of the Hermitian curve is also presented.
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if…
In this paper we introduce the notion of $n$-permutation numerical semigroup. While there are just three $2$-permutation numerical semigroups, there are infinitely many $n$-permutation numerical semigroups if $n > 2$. We construct $16$…
Let n_g denote the number of numerical semigroups of genus g. Bras-Amoros conjectured that n_g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree.…
A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…
We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by…
This paper presents an algebraic construction of families of unitary matrices that achieve full diversity. They are obtained as subsets of cyclic division algebras.
We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.
Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…
We realize any submultiplicative increasing function which is equivalent to a polynomial proportion of itself as the growth function of a finitely generated simple Lie algebra. As an application, we resolve two open problems posed by…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
We survey new results on finite groups of birational transformations of algebraic varieties.