Points and Lines Configurations for Perpendicular Bisectors of Convex Cyclic Polygons
Copyright policy )Points and Lines Configurations for Perpendicular Bisectors of Convex Cyclic Polygons
We characterize the topological configurations of points and lines that may arise when placing $n$ points on a circle and drawing the $n$ perpendicular bisectors of the sides of the corresponding convex cyclic $n$-gon. We also provide exact and asymptotic formulas describing a random realizable configuration, obtained either by sampling the points uniformly at random on the circle or by sampling a realizable configuration uniformly at random.
Probability measures on topological spaces, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Combinatorial probability, Computer Sciences, Probability (math.PR), Exact enumeration problems, generating functions, Metric Geometry (math.MG), random realizable configuration, Other designs, configurations, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Datavetenskap (datalogi), Mathematics - Metric Geometry, FOS: Mathematics, Mathematics - Combinatorics, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], Combinatorics (math.CO), Mathematics - Probability
Probability measures on topological spaces, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Combinatorial probability, Computer Sciences, Probability (math.PR), Exact enumeration problems, generating functions, Metric Geometry (math.MG), random realizable configuration, Other designs, configurations, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Datavetenskap (datalogi), Mathematics - Metric Geometry, FOS: Mathematics, Mathematics - Combinatorics, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], Combinatorics (math.CO), Mathematics - Probability
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