Distinct distances on two lines
نویسندگان
چکیده
Let P1 and P2 be two finite sets of points in the plane, so that P1 is contained in a line l1, P2 is contained in a line l2, and l1 and l2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs of P1 × P2 is Ω (
منابع مشابه
Distinct distances between points and lines
We show that for m points and n lines in R2, the number of distinct distances between the points and the lines is Ω(m1/5n3/5), as long as m1/2 ≤ n ≤ m2. We also prove that for any m points in the plane, not all on a line, the number of distances between these points and the lines that they span is Ω(m4/3). The problem of bounding the number of distinct point-line distances can be reduced to the...
متن کاملDistinct Distances Between Sets of Points on a Line and a Hyperplane in R
A variant of Erdős’s distinct distances problem considers two sets of points in Euclidean space P1 and P2, both of cardinality n, and asks whether we can find a superlinear bound on the number of distinct distances between all pairs of points with one in P1 and the other in P2. In 2013, Sharir, Sheffer, and Solymosi [8] showed a lower bound of Ω(n) when P1 and P2 are both collinear point sets i...
متن کاملAssessing Genetic Diversity in Iranian Native Silkworm (Bombyx mori L.) Strains and Japanese Commercial Lines Using AFLP Markers
Three Iranian native strains and three Japanese commercial lines of the silkworm Bombyx mori were analyzed using amplified fragment length polymorphism (AFLP) markers. A set of ten PstI/TaqI primer combinations amplified a total of 322 bands out of which 251 (%78) were polymorphic. Estimates of Nei’s gene diversity for all loci in individual strains and commercial lines indicated a higher degre...
متن کاملFew distinct distances implies no heavy lines or circles
We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set P of n points determines o(n) distinct distances, then no line contains Ω(n) points of P and no circle contains Ω(n) points of P . We rely on the bipartite and partial variant of the Elekes-Sharir framework that was presented by Sharir, Sheffer, and Solymosi in [2...
متن کاملFault Location on Compensated Transmission Lines without Current Measurement
This paper presents a novel fault location method for series compensated transmission lines. It is established based on synchronized voltages sampling and Thevenin impedance from both ends of series compensated transmission line. The method is based on the use of phasor measurement units (PMU) technology which is aimed to be independent of current measurements, fault type, fault resistance, fau...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 120 شماره
صفحات -
تاریخ انتشار 2013