A143107 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, i.e., of degree 2n-3.

0, 1, 1, 2, 4, 2, 4, 8, 4, 2, 24, 2

Offset

1,4

Comments

It is unknown if this sequence is bounded. For all n >= 4, a(n) is at least two. It is unknown if it is 2 for infinitely many n. It is unknown if it is always even for all n >= 2. Note that 2n-3 appears in A143106 if and only if a(n) is 1 or 2.

Links

Table of n, a(n) for n=1..12.

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 line arxiv 1302.1441 [math.AC], 2013.

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

Example

a(3) = 1 as x^3 + 3xy + y^3 is the unique polynomial in H(2,d) with 3 terms and of maximum degree (in this case 3).

Mathematica

See the paper by Lebl and Lichtblau.

Crossrefs

Cf. A143106, A143108, A143109.

Sequence in context: A286536 A318768 A166242 * A051638 A286580 A286598

Adjacent sequences: A143104 A143105 A143106 * A143108 A143109 A143110

Keyword

nonn,more

Author

Jiri Lebl, Jul 25 2008

Extensions

One more term (24), added addendum to and corrected title of paper - Jiri Lebl, Feb 08 2013

Added another term (2) that was computed in the newer version of the addendum. Edited by Jiri Lebl, May 02 2014

Status

approved