Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool the study of regular Cayley maps and, more generally, finite groups with complementary factorisation $G=BY$, where $Y$ is cyclic and core-free in $G$. In this paper, we classify all examples $B$ monolithic (meaning that it has unique minimal normal subgroup, subgroup not abelian) As consequence, obtain classif...

<p style='text-indent:20px;'>In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing construction, the ring <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{F}_{j, k} $\end{document}</tex-math></inline-formula> and its associated Gray maps, show how one can construct of length id="M2">\...

Modern computing system applications or workloads can bring significant non-uniform temperature gradient on-chip, and hence can cause significant temperature uncertainty during clock-tree synthesis. Existing designs of clock-trees have to assume a given time-invariant worst-case temperature map but cannot deal with a set of temperature maps under a set of workloads. For robust clock-tree synthe...

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomor...

We classify all embeddings θ : PG(n,K) −→ PG(d,F), with d ≥ n(n+3) 2 and K,F skew fields with |K| > 2, such that θ maps the set of points of each line of PG(n,K) to a set of coplanar points of PG(d,F), and such that the image of θ generates PG(d,F). It turns out that d = 12n(n+ 3) and all examples “essentially” arise from a similar “full” embedding θ′ : PG(n,K) −→ PG(d,K) by identifying K with ...

We consider multi-variable functions defined over a fixed finite set A. A centralizing monoid M is a set of unary functions on A which commute with all members of some set F of functions on A, where F is called a witness of M . We show that every centralizing monoid has a witness whose arity does not exceed |A|. Then we present a method to count the number of centralizing monoids which have set...