Addendum to Uniqueness of certain polynomials constant on a line

TL;DR

This paper extends computational classification of sharp polynomials constant on a line to degrees 19 and 21, revealing a large variety at degree 19 and uniqueness at degree 21.

Contribution

It provides new computational results for degrees 19 and 21, showing a surprising diversity at degree 19 and uniqueness at degree 21.

Findings

13 sharp polynomials at degree 19

Only the group invariant polynomial at degree 21

Extension of classification to higher degrees

Abstract

The computer calculations in arXiv:0808.0284 to classify sharp polynomials with nonegative coefficients constant on the line $x+y=1$ have been extended to degrees 19 and 21. In degree 19 a surprisingly large number of 13 sharp polynomials was found, while in degree 21 only the group invariant polynomial exists.