Uniqueness of certain polynomials constant on a line

Details Uniqueness of certain polynomials constant on a line Uniqueness of certain polynomials constant on a line

2008-08-03

arxiv.org/abs/0808.0284v3

Linear Algebra and Its Applications 433 (2010) pp. 824-837

Mathematics

Complex Variables

20 pages, latex; removed section 10 and address referee suggestions; accepted to Linear Algebra and its Applications

Scientific paper

10.1016/j.laa.2010.04.020

We study a question with connections to linear algebra, real algebraic geometry, combinatorics, and complex analysis. Let $p(x,y)$ be a polynomial of degree $d$ with $N$ positive coefficients and no negative coefficients, such that $p=1$ when $x+y=1$. A sharp estimate $d \leq 2N-3$ is known. In this paper we study the $p$ for which equality holds. We prove some new results about the form of these "sharp" polynomials. Using these new results and using two independent computational methods we give a complete classification of these polynomials up to $d=17$. The question is motivated by the problem of classification of CR maps between spheres in different dimensions.

Affiliated with

Also associated with

No associations

Rating

Uniqueness of certain polynomials constant on a line 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 Uniqueness of certain polynomials constant on a line, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniqueness of certain polynomials constant on a line will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-626109