cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

This page as a plain text file.
%I A143109 #37 Aug 13 2025 17:02:57
%S A143109 0,0,0,11,38,88,198
%N 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.
%C A143109 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).
%C A143109 Likely an erroneous version of A387029. - _Sean A. Irvine_, Aug 13 2025
%H A143109 J. P. D'Angelo, Simon Kos and Emily Riehl, <a href="http://dx.doi.org/10.1007/BF02921879">A sharp bound for the degree of proper monomial mappings between balls</a>, J. Geom. Anal., 13(4):581-593, 2003.
%H A143109 J. P. D'Angelo and J. Lebl, <a href="http://arXiv.org/abs/0708.3232">Complexity results for CR mappings between spheres</a>, arXiv:0708.3232 [math.CV], 2008.
%H A143109 J. P. D'Angelo and J. Lebl, <a href="http://dx.doi.org/10.1142/S0129167X09005248">Complexity results for CR mappings between spheres</a>, Internat. J. Math. 20 (2009), no. 2, 149-166.
%H A143109 J. Lebl and D. Lichtblau, <a href="http://arxiv.org/abs/0808.0284">Uniqueness of certain polynomials constant on a hyperplane</a>, arXiv:0808.0284 [math.CV], 2008-2010.
%H A143109 J. Lebl and D. Lichtblau, <a href="http://dx.doi.org/10.1016/j.laa.2010.04.020">Uniqueness of certain polynomials constant on a hyperplane</a>, Linear Algebra Appl., 433 (2010), no. 4, 824-837
%t A143109 (* See the paper by Lebl-Lichtblau. *)
%Y A143109 Cf. A143107, A143108, A387029.
%K A143109 hard,nonn
%O A143109 1,4
%A A143109 Jiri Lebl (jlebl(AT)math.uiuc.edu), Jul 25 2008