Abstract
Let ℋ be a collection ofn hyperplanes ind-space in general position. For each tuple ofd+1 hyperplanes of ℋ consider the open ball inscribed in the simplex that they form. Let ℬk denote the number of such balls intersected by exactlyk hyperplanes, fork=0, 1,...,n−d−1. We show that
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Work on this paper by the second author has been supported by National Science Foundation Grant DMS-91-03126. Work by the third and fourth authors has been supported by National Science Foundation Grant CCR-89-01484. Work by the third author has also been supported by Hungarian Science Foundation Grant OTKA-1814. Work by the fourth author has also been supported by Office of Naval Research Grant N00014-90-J-1284, and by grants from the U.S.-Israeli Binational Science Foundation, the G.I.F.—the German Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences.
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Aronov, B., Naiman, D.Q., Pach, J. et al. An invariant property of balls in arrangements of hyperplanes. Discrete Comput Geom 10, 421–425 (1993). https://doi.org/10.1007/BF02573987
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DOI: https://doi.org/10.1007/BF02573987