Related papers: Classifying bent functions by their Cayley graphs
You can invent striking and challenging problems with unique solution by building some symmetry into functional equations. Some are suitable for high school; others could generate college-level projects involving computer algebra. The…
We give a new simple construction for known binary quadratic symmetric bent and almost bent functions. In particular, for even number of variables, they are self-dual and anti-self-dual quadratic bent functions, respectively, which are not…
We show that the large Cartesian powers of any graph have log-concave valencies with respect to a ffxed vertex. We show that the series of valencies of distance regular graphs is log-concave, thus improving on a result of (Taylor,…
The main purpose of this paper is to introduce various convexity concepts in terms of a positive Chebyshev system $\omega$ and give a systematic investigation of the relations among them. We generalize a celebrated theorem of…
Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…
We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle…
Perfect code in Cayley graphs and Cayley sum graphs is studied extensively in recent years. In this paper, we consider perfect code in generalized Cayley graphs.
Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…
The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.
This paper investigates the coloring problem on Fibonacci-Cayley tree, which is a Cayley graph whose vertex set is the Fibonacci sequence. More precisely, we elucidate the complexity of shifts of finite type defined on Fibonacci-Cayley tree…
We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/<q>, where q is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including…
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
It is well-known that degree two finite field extensions can be equipped with a Hermitian-like structure similar to the extension of the complex field over the reals. In this contribution, using this structure, we develop a modular…
If $f(x,y)$ is a real function satisfying $y>0$ and $\sum_{r=0}^{n-1}f(x+ry,ny)=f(x,y)$ for $n=1,2,3,\ldots$, we say that $f(x,y)$ is an invariant function. Many special functions including Bernoulli polynomials, Gamma function and Hurwitz…
The purpose of this paper is to study a generalization of strongly $\eta$-convex functions using the fractal calculus developed by Yang \cite{Yang}, namely generalized strongly $\eta$-convex function. Among other results, we obtain some…
For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other…
In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function…
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann zeta function at positive odd-integer arguments. The explicit expressions enable us to obtain criteria for the dimension of the vector space…
In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.
The chain relation, due to Conley, and the strong chain relation, due to Easton, are well studied for continuous maps on compact metric spaces. Following Fathi and Pageault, we use barrier functions to generalize the theory to general…