We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].
Let be a fixed symmetric finite subset of that generates a Zariski dense subgroup of when we consider it as an algebraic group over by restriction of scalars. We prove that the Cayley graphs of with respect to the projections of is an expander family if ranges over square-free ideals of if and is an arbitrary numberfield, or if and .
In this paper we analyze the computational complexity of a processor optimization problem. Given operations with interval times in a branching flow graph, the problem is to find an assignment of the operations to a minimum number of processors. We analyze the complexity of this assignment problem for flow graphs with a constant number of program traces and a constant number of processors.
There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli, Gosper and Srivastava. In this paper, we extend some of them. Namely, we give the exponential generating function of hyperharmonic numbers indexed by arithmetic progressions; in the sum several combinatorial numbers (like Stirling and Bell numbers) and the hypergeometric function appear.