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.

0, 0, 3, 4, 10, 24, 32, 56

Offset: 1

Author

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

Keywords

• hard
• nonn
• more

Comments

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

Links

• Carlos Améndola, Viet Duc Nguyen, and Janike Oldekop, One-dimensional Discrete Models of Maximum Likelihood Degree One, arXiv:2507.18686 [math.ST], 2025. See p. 24.
• John 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.
• John P. D'Angelo and Jiří Lebl, Complexity results for CR mappings between spheres, arXiv:0708.3232 [math.CV], 2008.
• John P. D'Angelo and Jiří Lebl, Complexity results for CR mappings between spheres, Internat. J. Math. 20 (2009), no. 2, 149-166.
• Jiří Lebl and Daniel Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, arXiv:0808.0284 [math.CV], 2008-2010.
• Jiří Lebl and Daniel Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, Linear Algebra Appl., 433 (2010), no. 4, 824-837

Crossrefs

Cf. A143107, A143109.

Programs

Mathematica

See the paper by Lebl-Lichtblau.

Formula

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 ).