Anderson, James W. Parlier, Hugo Pettet, Alexandra 2010-10-27 We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus g which fill and pairwise intersect at most Kgreater-or-equal, slanted1 times is View the MathML source as g→∞. We then bound from below the cardinality of a filling set of systoles by g/log(g). This illustrates that the topological condition that a set of curves pairwise intersect at most once is quite far from the geometric condition that such a set of curves can arise as systoles. application/pdf https://folia.unifr.ch/global/documents/301702 https://folia.unifr.ch/documents/301702/files/par_sfs.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.topol.2010.10.007 info:eu-repo/semantics/openAccess License undefined Topology and its Applications. - 2011, vol. 158, no. 1, p. 84-92 Systoles Simple curves on surfaces info:eu-repo/classification/udc/51 Small filling sets of curves on a surface http://purl.org/coar/resource_type/c_6501