Abstract
We give the asymptotic growth of the number of arcs of bounded length between boundary components on hyperbolic surfaces with boundary. Specifically, if S has genus g , n boundary components and p punctures, then the number of orthogeodesic arcs in each pure mapping class group orbit of length at most L is asymptotic to L^{6g-6+2(n+p)} times a constant. We prove an analogous result for arcs between cusps, where we define the length of such an arc to be the length of the sub-arc obtained by removing certain cuspidal regions from the surface.
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