Maximum hitting for n sufficiently large

For a left-compressed intersecting family \A contained in [n]^(r) and a set X contained in [n], let \A(X) = {A in \A : A intersect X is non-empty}. Borg asked: for which X is |\A(X)| maximised by taking \A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.Comment: Version 2 corrects the calculation of the sizes of the set families appearing in the proof of the main theorem. It also incorporates a number of other smaller corrections and improvements suggested by the anonymous referees. 7 page

Domain Number Distribution in the Nonequilibrium Ising Model

We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted domain, $Q_1(t)\sim t^{-\delta}$, are characterized by two independent nontrivial exponents. We develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents.Comment: 9 pages, 4 figures, revte