We study Boolean routing on Cayley networks. Let K (M G) denote the Kolmogorov complexity of the multiplication table of a group G of order n. We show that O(maxfd logn; K (M G)g) memory bits per local router (hence a total of O(n maxfd logn; K (M G)g) memory bits) are suucient to do Boolean routing on the Cayley network constructed from the group G and a set of d generators. It is a consequenc...

Suppose that  is a finite group. Then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . Suppose that . Then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if  is a group such that , where , then . Here  denotes the family of Suzuk...

We construct a nite-dimensional vector space of functions of two complex variables attached to a smooth algebraic curve C over a nite eld Fq , q odd, and a level. These functions collect the analytic information about the cohomology of the curve and its quadratic twists that is encoded in the corresponding L-functions; they are double Dirichlet series in two independent complex variables s;w. W...

Any diagram group over a +nite semigroup presentation acts properly, freely, and cellularly by isometrices on a proper CAT(0) cubical complex. The existence of a proper, cellular action by isometries on a CAT(0) cubical complex has powerful consequences for the acting group G. One gets, for example, a proof that G satis+es the Baum–Connes conjecture. Any diagram group over a +nite presentation ...

To Charlie Curtis Contents 0. Introduction 1. Notation, prerequisites and complements A. Generic nite reductive groups Usual invariants of a generic nite reductive group Class functions on G d{split Levi subgroups B. Generic characters Some consequences of Lusztig's results Generic unipotent characters, uniform functions The generic Deligne{Lusztig induction and restriction 2. d{cuspidality and...

Let G be a connected noncompact simple Hermitian symmetric group with nite center. Let H() denote the geometric realization of an irreducible unitary highest weight representation with highest weight. Then H() consists of vector-valued holomorphic functions on G=K and the action of G on H() is given in terms of a factor of automorphy. For highest weights corresponding to ladder representations,...

Throughout this paper D always will denote a design with v points, k > 2 points per line, and = 1 line through any two diierent points. Let G Aut (D). I will primarily be interested in the case in which G either is 2-transitive on the points of D or is transitive on the ags (incident point-line pairs) of D. Note that 2-transitivity implies ag-transitivity since = 1. The subject matter has been ...

Answering two problems formulated by Marcus and P aun, we prove that it is decidable whether or not a context-free language can be written as the set of all nite pre xes of an in nite word and that it is decidable whether or not a regular language can be written as the set of all nite subwords of an in nite word. TUCS Research Group Mathematical Structures of Computer Science