Groups Having a Maximum Number of Independent Generators

on the number of maximum independent sets of graphs

let $g$ be a simple graph. an independent set is a set ofpairwise non-adjacent vertices. the number of vertices in a maximum independent set of $g$ isdenoted by $alpha(g)$. in this paper, we characterize graphs $g$ with $n$ vertices and with maximumnumber of maximum independent sets provided that $alpha(g)leq 2$ or $alpha(g)geq n-3$.

Bounds on the Number of Vectors Having a Specified Maximum

Code Division Multiple Access (CDMA) technology allows a large number of mobile radio users to share limited bandwidth simultaneously. This is achieved by spreading individual users’ signals over available bandwidth with orthogonal spreading codes—the orthogonality of the spreading codes allows individual signals to be distinguished. The effective use of bandwidth in this system is a considerab...

Integer Sets Having the Maximum Number of Distinct Differences

In this paper we study the function D(k, n) which is the maximum of |A − A| = ∣{a − b : a, b ∈ A} ∣∣ over all k-subsets A of {0, . . . , n}. We prove that for any fixed real c ≥ 0 and any function k(n) = (c + o(1)) √ n, the limit d(c) = lim n→∞ D(k(n), n) n exists, as well as present some upper and lower bounds on d(c).

Random-number Generators Physical Random-number Generators

R andom numbers have applications in many areas: simulation, game-playing, cryptography, statistical sampling, evaluation of multiple integrals, particletransport calculations, and computations in statistical physics, to name a few. Since each application involves slightly different criteria for judging the “worthiness” of the random numbers generated, a variety of generators have been develope...

The Maximum Number of Edges in a Strongly Multiplicative Graph