which is Artin’s braid relation. In general we will refer to (1) as the braid relation satisfied by si and sj. In order for W to be a Coxeter group it is required that the given set of relations between elements of I give a presentation of W . Informally, this means that any relation between generators in I can be deduced from the fact that the s ∈ Σ have order 2 and the braid relations. Formal...

We study birational monomial transformations of the form φ(x : y : z) = (ε1x1y1z1 : ε2x2y2z2 : xα3yβ3zγ3), where ε1,ε2 ∈ {−1,1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ, we prove a formula, which represents the transformationφ as a product of generators of the group. To prove this formula, we use birati...

Abstract—In this work we present two generators for the group of symmetries of the generic (m+1) dimensional periodic Costas arrays over elementary abelian (Zp)m groups: one that is defined by multiplication on m dimensions and the other by shear (addition) on m dimensions. Through exhaustive search we observe that these two generators characterize the group of symmetries for the examples we we...

Intuitively, a pseudorandom generator (PRG) is a procedure that generates a pseudorandom distribution. A PRG shares the parameters of the underlying pseudorandom distribution: the class A of algorithms to which the generated distribution looks random, and a bound on how different the pseudorandom distribution can look from the uniform one for algorithms from A. Definition 1 (Pseudorandom genera...