The classical hypergraph Ramsey number rk(s, n) is the minimum N such that for every redblue coloring of the k-tuples of {1, . . . , N}, there are s integers such that every k-tuple among them is red, or n integers such that every k-tuple among them is blue. We survey a variety of problems and results in hypergraph Ramsey theory that have grown out of understanding the quantitative aspects of r...

Abstract. We discuss in some detail the general problem of computing averages of convergent Euler products, and apply this to examples arising from singular series for the k-tuple conjecture and more general problems of polynomial representation of primes. We show that the “singular series” for the k-tuple conjecture have a limiting distribution when taken over k-tuples with (distinct) entries ...

A Roman dominating function (RDF) on a digraph $D$ is a function $f: V(D)rightarrow {0,1,2}$ satisfying the condition that every vertex $v$ with $f(v)=0$ has an in-neighbor $u$ with $f(u)=2$. The weight of an RDF $f$ is the value $sum_{vin V(D)}f(v)$. The Roman domination number of a digraph $D$ is the minimum weight of an RDF on $D$. A set ${f_1,f_2,dots,f_d}$ of Roman dominating functions on ...

Given a simple graph G = (V, E) and a fixed positive integer k. In a graph G, a vertex is said to dominate itself and all of its neighbors. A set D ⊆ V is called a k-tuple dominating set if every vertex in V is dominated by at least k vertices of D. The k-tuple domination problem is to find a minimum cardinality k-tuple dominating set. This problem is NP-complete for general graphs. In this pap...

Network lifetime is a critical issue in wireless sensor networks. In the coverage problem, sensors can be partitioned into many subsets to prolong network lifetime. These subsets are activated successively and each of them completely covers an interest region. Many centralized algorithms have been proposed to solve this problem. A very few distributed versions have also been presented but none ...

Let an (r, s)-formation be a concatenation of s permutations of r distinct letters, and let a block of a sequence be a subsequence of consecutive distinct letters. A k-chain on [1,m] is a sequence of k consecutive, disjoint, nonempty intervals of the form [a0, a1][a1 + 1, a2] . . . [ak−1 + 1, ak] for integers 1 6 a0 6 a1 < . . . < ak 6 m, and an s-tuple is a set of s distinct integers. An s-tup...