In the nineties, A.G. Spera introduced a construction principle for divisible designs. Using this method, we get series of divisible designs from finite Laguerre geometries. We show a close connection between some of these divisible designs and divisible designs whose construction was based on a conic in a plane of a 3-dimensional projective space.

A divisible design graph is a graph whose adjacency matrix is the incidence matrix of a divisible design. Divisible design graphs are a natural generalization of (v, k, λ)-graphs, and like (v, k, λ)-graphs they make a link between combinatorial design theory and algebraic graph theory. The study of divisible design graphs benefits from, and contributes to, both parts. Using information of the e...

Example 1 Lets consider the integers from 1 to 10,000. The properties are defined as follows: E1 = property that an integer is divisible by 4 E2 = property that an integer is divisible by 5 E3 = property that an integer is divisible by 6 The probabilities of individual divisability are easily computed: Pr [E1] = probability the number is divisible by 4 = 1=4 Pr [E2] = probability the number is ...

Recently, some divisible electronic cash (e-cash) systems have been proposed. However, in existing divisible e-cash systems, efficiency or unlinkability is not sufficiently accomplished. In the existing efficient divisible cash systems, all protocols are conducted in the order of the polynomial of logN where N is the divisibility precision (i.e., (the total coin amount)/ (minimum divisible unit...

Divisible design digraphs are constructed from skew balanced generalized weighing matrices and Hadamard matrices. Commutative non-commutative association schemes shown to be attached the divisible digraphs.

The algebraic structure of divisible abelian semigroups has been studied in [9] and [l]. Some results on the topological and algebraic structure of compact uniquely divisible abelian semigroups have been obtained in [4] and [5]. A statement of equivalent conditions for a compact abelian semigroup to be divisible is presented in the present paper. Some of the results in [4] are extended to subun...

We introduce the concept of a (p; d)-divisible problem, where p reeects the number of processors and d the number of communication phases of a parallel algorithm solving the problem. We call problems that are recursively (n ; O(1))-divisible in a work-optimal way with 0 < < 1 ideally divisible and give motivation drawn from parallel computing for the relevance of that concept. We show that seve...