TY - GEN

T1 - On triple intersections of three families of unit circles

AU - Raz, Orit E.

AU - Sharir, Micha

AU - Solymosi, József

PY - 2014

Y1 - 2014

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, Simonovits, and Szabó [4]. The problem is a special instance of a more general problem studied by Elekes and Szabó [5] (and by Elekes and Rónyai [3]).

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, Simonovits, and Szabó [4]. The problem is a special instance of a more general problem studied by Elekes and Szabó [5] (and by Elekes and Rónyai [3]).

KW - Combinatorial geometry

KW - Incidences

KW - Polynomials

KW - Unit circles

UR - http://www.scopus.com/inward/record.url?scp=84904409212&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/2582112.2582149

DO - https://doi.org/10.1145/2582112.2582149

M3 - Conference contribution

SN - 9781450325943

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 198

EP - 205

BT - Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014

T2 - 30th Annual Symposium on Computational Geometry, SoCG 2014

Y2 - 8 June 2014 through 11 June 2014

ER -