50,745 research outputs found
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, , and an unreacted domain, , 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
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