Counting joints with multiplicities

Details Counting joints with multiplicities Counting joints with multiplicities

2012-03-16

arxiv.org/abs/1203.3735v1

Mathematics

Combinatorics

Scientific paper

Let $\mathfrak{L}$ be a collection of $L$ lines in $\R^3$ and $J$ the set of joints formed by $\mathfrak{L}$, i.e. the set of points each of which lies in at least 3 non-coplanar lines of $\mathfrak{L}$. It is known that $|J| \lesssim L^{3/2}$ (first proved by Guth and Katz). For each joint $x \in J$, let the multiplicity $N(x)$ of $x$ be the number of triples of non-coplanar lines through $x$. We prove here that $\sum_{x \in J}N(x)^{1/2} \lesssim L^{3/2}$, while in the last section we extend this result to real algebraic curves of bounded degree in $\R^3$, as well as to curves in $\R^3$ parametrised by polynomials of bounded degree.

Affiliated with

Also associated with

No associations

Rating

Counting joints with multiplicities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting joints with multiplicities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting joints with multiplicities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-352053