

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 2n5.


2




OFFSET

1,4


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 2n6, then there are infinitely many if any exist in H(2,d).


LINKS

Table of n, a(n) for n=1..7.
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):581593, 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, 149166.
J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, arXiv:0808.0284 [math.CV], 20082010.
J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, Linear Algebra Appl., 433 (2010), no. 4, 824837


MATHEMATICA

See the paper by LeblLichtblau.


CROSSREFS

Cf. A143107, A143108.
Sequence in context: A063146 A139276 A010002 * A007585 A024202 A213775
Adjacent sequences: A143106 A143107 A143108 * A143110 A143111 A143112


KEYWORD

hard,nonn


AUTHOR

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


STATUS

approved



