cp's OEIS Frontend

A143108 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 1, i.e., of degree 2n-4.

%I A143108 #26 Aug 12 2025 00:06:17
%S A143108 0,0,3,4,10,24,32,56
%N A143108 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 1, i.e., of degree 2n-4.
%C A143108 a(n) is also the number of fundamental one-dimensional discrete statistical models with rational maximum likelihood estimator supported on n states and of degree 2n-4. - _Carlos Améndola_, Aug 05 2025
%H A143108 Carlos Améndola, Viet Duc Nguyen, and Janike Oldekop, <a href="https://arxiv.org/abs/2507.18686">One-dimensional Discrete Models of Maximum Likelihood Degree One</a>, arXiv:2507.18686 [math.ST], 2025. See p. 24.
%H A143108 John 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 A143108 John P. D'Angelo and Jiří Lebl, <a href="http://arXiv.org/abs/0708.3232">Complexity results for CR mappings between spheres</a>, arXiv:0708.3232 [math.CV], 2008.
%H A143108 John P. D'Angelo and Jiří 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 A143108 Jiří Lebl and Daniel 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 A143108 Jiří Lebl and Daniel 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
%F A143108 Possibly can be computed from A143107 except for the third term, but this is not proved. Let b_n be elements of A143107, then a_n = 2 ( b_2 b_{n-1} + b_3 b_{n-2} + ... + b_{n-1} b_2 ).
%t A143108 See the paper by Lebl-Lichtblau.
%Y A143108 Cf. A143107, A143109.
%K A143108 hard,nonn,more
%O A143108 1,3
%A A143108 Jiri Lebl (jlebl(AT)math.uiuc.edu), Jul 25 2008