相关论文: On balanced characteristic functions of canonical …

A well-known conjecture due to van Lint and MacWilliams states that if $A$ is a subset of $\mathbb{F}_{q^2}$ such that $0,1 \in A$, $|A|=q$, and $a-b$ is a square for each $a,b \in A$, then $A$ must be the subfield $\mathbb{F}_q$. This…

A balanced graph is a bipartite graph with no induced circuit of length 2 mod 4. These graphs arise in linear programming. We focus on graph-algebraic properties of balanced graphs to prove a complete classification of balanced Cayley…

We quantize the regularity properties of classical graphs that determine spin models for singly-generated Yang-Baxter planar algebras, including the Kauffman polynomial, and construct explicit examples. A source of examples comes from…

Paley graphs are Cayley graphs which are circulant and strongly regular. Paley-type graph of order a product of two distinct Pythagorean primes was introduced by Dr Angsuman Das. In this paper, we extend the study of Paley-type graphs to…

The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto mutually orthogonal subspaces of piecewise polynomial functions on the cube $ I^d. $ This assertion provides an upper estimate for the…

Paley's theorem about lacunary coefficients of functions in the classical space $H^1$ on the unit circle is equivalent to the statement that certain Hankel matrices define bounded operators on $\ell^2$ of the nonnegative integers. Since…

We introduce the concept of a clique bitrade, which generalizes several known types of bitrades, including latin bitrades, Steiner $T(k-1,k,v)$ bitrades, extended $1$-perfect bitrades. For a distance-regular graph, we show a one-to-one…

Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general…

The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with…

A generalised Paley map is a Cayley map for the additive group of a finite field F, with a subgroup S=-S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the…

We show that the expected number of cliques in the Erd\H{o}s-R\'enyi random graph $G(n,p)$ is $n^{\frac1{-2\log p}(\log n-2\log\log n+O(1))}$.

The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G) + mu(G) equals its order, then G is a Koenig-Egervary graph. We call G…

In this paper we consider particular graphs defined by $\overline{\overline{\overline{K_{\alpha_1}}\cup K_{\alpha_2}}\cup\cdots \cup K_{\alpha_k}}$, where $k$ is even, $K_\alpha$ is a complete graph on $\alpha$ vertices, $\cup$ stands for…

We analyze the number of cliques of given size and the size of the largest clique in tensor product $G \times H$ of two Erd\H{o}s-R\'enyi graphs $G$ and $H$. Then an extended clustering coefficient is introduced and is studied for $G \times…

In this work, we establish two main results in the context of arithmetic and geometric properties of plane curves. First, we construct numerous new examples of arithmetic Zariski pairs and multiplets, where only a few ones were previously…

A result due to Gy\'arf\'as, Hubenko, and Solymosi (answering a question of Erd\"os) states that if a graph $G$ on $n$ vertices does not contain $K_{2,2}$ as an induced subgraph yet has at least $c\binom{n}{2}$ edges, then $G$ has a…

The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G)+mu(G) equals its order, then G is a Konig-Egervary graph. In this paper…

A discrete analog of quantum unique ergodicity was proved for Cayley graphs of quasirandom groups by Magee, Thomas and Zhao. They show that for large graphs there exist real orthonormal basis of eigenfunctions of the adjacency matrix such…

In 1976 Erdos, Kleitman and Rothschild determined the number of graphs without a clique of size $\ell$. In this note we extend their result to the case of forbidden cliques of increasing size. More precisely we prove that for $\ell_n \le…

We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale $U^{t,s}_p$ of anisotropic Banach spaces, under the conditions -1+1/p<s<-t<0 and -(r-1)+t<s,…