Minimal dilatation in Penner's construction

For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with punctures.Comment: 11 pages, 6 figure

Strangeness production as a function of charged particle multiplicity in proton-proton collisions

Recent measurements performed in high-multiplicity proton-proton (pp) and proton-lead (p-Pb) collisions have shown features that are reminiscent of those observed in lead-lead (Pb-Pb) collisions. These observations warrant a comprehensive measurement of the production of identified particles. We report on the production of \allparts at mid-rapidity measured as a function of multiplicity in pp collisions at $\sqrt{s}$ = 7 TeV with the ALICE experiment. Spectral shapes studied both for individual particles and via particle ratios such as ($\Lambda/K^{0}_{S}$) as a function of $p_{T}$ exhibit an evolution with event multiplicity and the production rates of hyperons are observed to increase more strongly than those of non-strange hadrons. These phenomena are qualitatively similar to the ones observed in p-Pb and Pb-Pb collisions

Signature, positive Hopf plumbing and the Coxeter transformation

By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.Comment: 16 pages, 5 figures, with appendix by Peter Feller and Livio Liecht