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 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. 3
 0, 1, 1, 2, 4, 2, 4, 8, 4, 2, 24, 2 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified April 24 04:23 EDT 2019. Contains 322406 sequences. (Running on oeis4.)