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A semigroup is called a generalized -semigroup if there exists a group congruence on such that the identity class contains a greatest element with respect to the natural partial order of . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup are determined. It is shown that a semigroup is a generalized -semigroup if and only if contains an anticone, which is a principal order ideal of . Also a characterization by means of the structure...
Hovey introduced A-cordial labelings in [4] as a simultaneous generalization of cordial and harmonious labelings. If A is an abelian group, then a labeling f: V(G) → A of the vertices of some graph G induces an edge-labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one.
Research on A-cordiality...
We study the family of closed Riemannian n-manifolds with holonomy group isomorphic to Z2n-1, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.
Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.
Following Lusztig, we consider a Coxeter group together with a weight function. Geck showed that the Kazhdan-Lusztig cells of are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of certain parabolic subgroups of are cells in the whole group, and we decompose the affine Weyl group of type into left...
An inflation of an algebra is formed by adding a set of new elements to each element in the original or base algebra, with the stipulation that in forming products each new element behaves exactly like the element in the base algebra to which it is attached. Clarke and Monzo have defined the generalized inflation of a semigroup, in which a set of new elements is again added to each base element, but where the new elements are allowed to act like different elements of the base, depending on the context...
We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.
We generalize the definition of quiver representation to arbitrary reductive groups. The classical definition corresponds to the general linear group. We also show that for classical groups our definition gives symplectic and orthogonal representations of quivers with involution inverting the direction of arrows.
Generalizations of the classical Schwarzian derivative of complex analysis have been proposed by Osgood and Stowe [12, 13], Carne [5], and Ahlfors [3]. We present another generalization of the Schwarzian derivative over vector spaces.
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