Abstract Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg’s count of unipotent elements, Rudvalis and Shindoda’s work on the fixed space of a random matrix, and Lusztig’s work on counting nilpotent matrices of ...

Cost complementarities arise from synergies in the production of heterogeneous goods. It is shown that synergies can be accounted for in terms of shared public inputs (roughly) if and only if synergies decrease as the scope of production increases. This case of ‘‘substitutive’’ synergies is argued to be typical. The key technical tool is a novel interpretation of conjugate Moebius inversion in ...

A generalized version of Groeneveld's convergence criterion for the virial expansion and generating functionals weighted $2$-connected graphs is proven. The works inhomogeneous systems yields bounds density expansions correlation functions $\rho_s$ (a.k.a. distribution or factorial moment measures) grand-canonical Gibbs measures with pairwise interactions. proof based on recurrence relations gr...

BACKGROUND Moebius syndrome is a rare disorder with minimum clinical criteria of congenital facial weakness in association with impairment in abduction of one or both eyes. Mirror movements are not known to be associated with Moebius syndrome. CASE REPORT We present three patients who meet minimum criteria for a diagnosis of Moebius syndrome and who also display mirror movements. DISCUSSION...