A143109 Let H(2,d) be the space of polynomials p(x,y) of two variables with nonnegative coefficients such that p(x,y)=1 whenever x + y = 1. a(n) is the number of different polynomials in H(2,d) with exactly n distinct monomials and of maximum degree minus two, i.e., of degree 2n-5.

0, 0, 0, 11, 38, 88, 198

Offset: 1

Author

Jiri Lebl (jlebl(AT)math.uiuc.edu), Jul 25 2008

Keywords

• hard
• nonn

Comments

It is unknown but conjectured that this is a sequence of finite numbers. Note that if we went one degree lower and look at polynomials of degree 2n-6, then there are infinitely many if any exist in H(2,d).

Likely an erroneous version of A387029. - Sean A. Irvine, Aug 13 2025

Links

• 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. P. D'Angelo and J. Lebl, Complexity results for CR mappings between spheres, arXiv:0708.3232 [math.CV], 2008.
• J. P. D'Angelo and J. Lebl, Complexity results for CR mappings between spheres, Internat. J. Math. 20 (2009), no. 2, 149-166.
• J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, arXiv:0808.0284 [math.CV], 2008-2010.
• J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, Linear Algebra Appl., 433 (2010), no. 4, 824-837

Crossrefs

Cf. A143107, A143108, A387029.

Programs

Mathematica

(* See the paper by Lebl-Lichtblau. *)