Uniqueness of certain polynomials constant on a line

Abstract

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 $d\le 2N-3$ 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.

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

References in corpus (2)

• Complexity results for CR mappings between spheres
• On the complexity of proper holomorphic mappings between balls

Cited by in corpus (3)

• Rational sphere maps, linear programming, and compressed sensing
• Addendum to Uniqueness of certain polynomials constant on a line
• Polynomials constant on a hyperplane and CR maps of hyperquadrics