A143106 Odd degrees for which (up to swapping of variables) there exists a unique polynomial p(x,y), such that p(x,y)=1 when x+y=1, with positive coefficients and such that the number of terms is minimal (equal to (d+3)/2). There always exists a group invariant polynomial (see any of the references), but for many degrees, other such extremal polynomials exist.
1, 3, 5, 9, 17, 21
Offset: 0
Examples
7 is not in the sequence as there are two noninvariant polynomials with minimal number of terms: x^7 + 7/2 xy + 7/2 x^5y + 7/2 xy^5 + y^7 and x^7 + 7 x^3y + 7 xy^3 + 7 x^3y^3 + y^7. This is beside the group invariant x^7 + 7 x^3y + 14 x^2y^3 + 7 xy^5 + y^7 (and one with x,y reversed).
Links
- J. P. D'Angelo and J. Lebl, Complexity results for CR mappings between spheres, Internat. J. Math. 20 (2009), no. 2, 149-166.
- J. P. D'Angelo and J. Lebl, Complexity results for CR mappings between spheres, arXiv:0708.3232 [math.CV], 2008.
- J. P. D'Angelo, Simon Kos and Emily Riehl, A sharp bound for the degree of proper monomial mappings between balls, J. Geom. Anal., 13(4):581-593, 2003.
- J. Lebl, Addendum to Uniqueness of certain polynomials constant on a hyperplane, preprint arXiv:1302:1441
- J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, arXiv:0808.0284 [math.CV]
- J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, Linear Algebra Appl., 433 (2010), no. 4, 824-837
Programs
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Mathematica
See the paper by Lebl-Lichtblau
Extensions
Added term 21 that was recently computed, see the recent preprint by Lebl. Added publication data for Lebl-Lichblau paper. Corrected and edited by Jiri Lebl, May 02 2014
Comments