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Search: id:A143107
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| A143107 |
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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. |
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4
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OFFSET
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1,4
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COMMENT
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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 one or 2.
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REFERENCES
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J. P. D'Angelo and J. Lebl. Complexity results for CR mappings between spheres. to appear in Internat. J. Math., preprint arXiv:0708.3232.
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 and D. Lichtblau. Uniqueness of certain polynomials constant on a hyperplane. preprint
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LINKS
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J. P. D'Angelo and J. Lebl. Complexity results for CR mappings between spheres, to appear in Internat. J. Math.
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EXAMPLE
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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)
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MATHEMATICA
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See the paper by Lebl-Lichtblau
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CROSSREFS
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Cf. A143106, A143108, A143109.
Sequence in context: A128859 A047975 A112791 this_sequence A166242 A051638 A155682
Adjacent sequences: A143104 A143105 A143106 this_sequence A143108 A143109 A143110
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KEYWORD
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nonn,more
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AUTHOR
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Jiri Lebl (jlebl(AT)math.uiuc.edu), Jul 25 2008
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