相关论文: Twin bent functions and Clifford algebras
After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix…
The distinguishing index $D'(G)$ of a graph $G$ is the least number of colours needed in an edge colouring which is not preserved by any non-trivial automorphism. Broere and Pil\'sniak conjectured that if every non-trivial automorphism of a…
We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph K_{s,t} which admits only the identity automorphism. In particular this allows us to determine the distinguishing number of the…
Coloring the arcs of biregular graphs was introduced with possible applications to industrial chemistry, molecular biology, cellular neuroscience, etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for…
We study a new problem for cubic graphs: bipartization of a cubic graph $Q$ by deleting sufficiently large independent set $I$. It can be expressed as follows: \emph{Given a connected $n$-vertex tripartite cubic graph $Q=(V,E)$ with…
A graph coloring has bounded clustering if each monochromatic component has bounded size. This paper studies such a coloring, where the number of colors depends on an excluded complete bipartite subgraph. This is a much weaker assumption…
Solving a conjecture of M. H. Freedman, L. Lov\'asz and A. Schrijver we prove that a graph parameter is edge reflection positive and multiplicative if and only if it can be represented by an edge coloring model.
Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new…
We prove that for any m > 1 given any m-tuple of Hecke eigenforms $f_i$ of level 1 whose weights satisfy the usual regularity condition there is a self-dual cuspidal automorphic form $\pi$ of $\GL_{2^m}(\Q)$ corresponding to their tensor…
We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph $\Lambda$ and a "code" assigned to each orbit of…
Given a real representation of the Clifford algebra corresponding to $R^{p+q}$ with metric of signature $(p,q)$, we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of $k$-forms on…
A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let $H_k(n,m)$ be a random $k$-uniform hypergraph on $n$ vertices formed by picking $m$ edges uniformly, independently…
We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…
We investigate a class of 2-edge coloured bipartite graphs known as alternating signed bipartite graphs (ASBGs) that encode the information in alternating sign matrices. The central question is when a given bipartite graph admits an…
We define Bergman presentations and Bergman algebras associated to Bergman presentations. These algebras embrace various generalisations of Leavitt path algebras. A Bergman presentation can be visualised by a Bergman graph, which is a…
Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a…
The concatenation of four Boolean bent functions $f=f_1||f_2||f_3||f_4$ is bent if and only if the dual bent condition $f_1^* + f_2^* + f_3^* + f_4^* =1$ is satisfied. However, to specify four bent functions satisfying this duality…
We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the complement of that of the other. We…
The main aim of the present paper is to introduce new methods for the study of combinatorial designs related to bent functions. They are based on interpretations of convolution on finite abelian groups as multiplication by a…
We introduce a class of left cancellative categories we call ordinal graphs for which there is a functor $d:\Lambda\rightarrow\mathrm{Ord}$ by which morphisms of $\Lambda$ factor. We use generators and relations to study the Cuntz-Krieger…