Related papers: Combinatorial properties and characterization of g…
Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of the displacement group, the other one by a property of the…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial…
The purpose of this paper is twofold. Firstly, we generalize the notion of characteristic polynomials of hyperplane and toric arrangements to those of certain abelian Lie group arrangements. Secondly, we give two interpretations for the…
We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the…
This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is…
Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…
In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…
We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.
In this paper we study the property of the Arf good subsemigroups of $\mathbb{N}^n$, with $n\geq2$. We give a way to compute all the Arf semigroups with a given collection of multiplicity branches. We also deal with the problem of…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
This work introduces a new kind of affine semigroups called $P$-semigroups. Within the framework of $\mathcal C$-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a $\mathcal…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…