1
vote
3answers
541 views

A limit from an Erdos paper

Hi, I need help to prove that, for $ N = \big\lfloor \frac{1}{2}n\log(n)+cn \big\rfloor $ with $c \in \mathbb R $ and $0 \leq k \leq n: $ $$ \lim_{n\rightarrow +\infty} \dbinom{n}{k} ...
3
votes
1answer
450 views

A question about the number of intersections of lines in $R^{3}$

Suppose I have n lines in $R^{3}$ with the conditions that: no 3 lines in one plane, no 3 lines intersect at one point, for fixed 2 lines, no 3 lines intersect these 2 lines at the same time. what is ...
4
votes
1answer
382 views

Degree reduction argument in Guth-Katz'sproof of Erdos distinct distance problem in the plane

In the middle of page 9 of http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf. They said " Now we select a random subset....choosing lines independently with probability $\frac{Q}{100}$. With ...
6
votes
2answers
805 views

Erdos distance problem n=12

The recent paper On the Erdos distinct distance problem in the plane Authors: Larry Guth, Nets Hawk Katz prodded me to get a non-trivial example. Here is what I cannot find: an example of 12 ...
24
votes
3answers
1k views

Does there exist a comprehensive compilation of Erdos's open problems?

Fan Chung and Ron Graham's book Erdos on Graphs: His Legacy of Unsolved Problems (A. K. Peters, 1998) collects together all of Erdos's open problems in graph theory that they could find into a single ...
21
votes
5answers
4k views

Erdos Conjecture on arithmetic progressions

Introduction: Let A be a subset of the naturals such that $\sum_{n\in A}\frac{1}{n}=\infty$. The Erdos Conjecture states that A must have arithmetic progressions of arbitrary length. Question: I ...