TY - JOUR
T1 - Homotheties and incidences
AU - Aiger, Dror
AU - Sharir, Micha
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/7
Y1 - 2018/7
N2 - We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R3, we are able to obtain refined and new bounds for the number of rich homotheties, and for the number of distinct equivalence classes, under homotheties, of k-element subsets of S, for any k≥3. We also discuss the extensions of these problems to three and higher dimensions.
AB - We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R3, we are able to obtain refined and new bounds for the number of rich homotheties, and for the number of distinct equivalence classes, under homotheties, of k-element subsets of S, for any k≥3. We also discuss the extensions of these problems to three and higher dimensions.
KW - Combinatorial geometry
KW - Homothety transformation
KW - Incidences
UR - http://www.scopus.com/inward/record.url?scp=85046366526&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2018.04.003
DO - 10.1016/j.disc.2018.04.003
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AN - SCOPUS:85046366526
SN - 0012-365X
VL - 341
SP - 2011
EP - 2017
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 7
ER -