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...

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.

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 ...

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.

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...

Bank of Canada working papers are theoretical or empirical works-in-progress on subjects in economics and finance. The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada. Abstract We study price posting with undirected search in a search-theoretic monetary model with divisible money and divisible goods. Ex ante homogeneo...

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...