On Weighted Sums of Numbers of Convex Polygons in Point Sets
Por:
Huemer, Clemens, Oliveros, Deborah, Perez-Lantero, Pablo, Torra, Ferran, Vogtenhuber, Birgit
Publicada:
1 sep 2022
Resumen:
Let S be a set of n points in general position in the plane, and let
X-k,X-l(S) be the number of convex k-gons with vertices in S that have
exactly l points of S in their interior. We prove several equalities for
the numbers X-k,X-l(S). This problem is related to the Erdos-Szekeres
theorem. Some of the obtained equations also extend known equations for
the numbers of empty convex polygons to polygons with interior points.
Analogous results for higher dimension are shown as well.
Filiaciones:
Huemer, Clemens:
Univ Politecn Cataluna, Dept Matemat, Barcelona, Spain
Oliveros, Deborah:
Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Juriquilla, Juriquilla, Mexico
Perez-Lantero, Pablo:
Univ Santiago Chile USACH, Fac Ciencia, Dept Matemat & Ciencia Comp, Santiago, Chile
Torra, Ferran:
Univ Politecn Cataluna, Dept Matemat, Barcelona, Spain
Vogtenhuber, Birgit:
Graz Univ Technol, Inst Software Technol, Graz, Austria
hybrid, Green Submitted
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