TY - JOUR
T1 - On Triple Intersections of Three Families of Unit Circles
AU - Raz, Orit E.
AU - Sharir, Micha
AU - Solymosi, József
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2015/10/13
Y1 - 2015/10/13
N2 - Let p1, p2, p3 be three distinct points in the plane, and, for i = 1, 2, 3, let Ci be a family of n unit circles that pass through pi. We address a conjecture made by Székely, and show that the number of points incident to a circle of each family is O(n11/6), improving an earlier bound for this problem due to Elekes et al. (Comb Probab Comput 18:691–705, 2009). The problem is a special instance of a more general problem studied by Elekes and Szabó (Combinatorica 32:537–571, 2012) [and by Elekes and Rónyai (J Comb Theory Ser A 89:1–20, 2000)].
AB - Let p1, p2, p3 be three distinct points in the plane, and, for i = 1, 2, 3, let Ci be a family of n unit circles that pass through pi. We address a conjecture made by Székely, and show that the number of points incident to a circle of each family is O(n11/6), improving an earlier bound for this problem due to Elekes et al. (Comb Probab Comput 18:691–705, 2009). The problem is a special instance of a more general problem studied by Elekes and Szabó (Combinatorica 32:537–571, 2012) [and by Elekes and Rónyai (J Comb Theory Ser A 89:1–20, 2000)].
KW - Combinatorial geometry
KW - Incidences
KW - Unit circles
UR - http://www.scopus.com/inward/record.url?scp=84945463311&partnerID=8YFLogxK
U2 - 10.1007/s00454-015-9734-6
DO - 10.1007/s00454-015-9734-6
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84945463311
SN - 0179-5376
VL - 54
SP - 930
EP - 953
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 4
ER -