The asymptotic leading term for maximum rank of ternary forms of a given degree
| Autor: | Alessandro De Paris |
|---|---|
| Přispěvatelé: | DE PARIS, Alessandro |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Value (computer science)
010103 numerical & computational mathematics Commutative Algebra (math.AC) 01 natural sciences Upper and lower bounds Combinatorics Mathematics - Algebraic Geometry Symmetric tensor FOS: Mathematics Discrete Mathematics and Combinatorics Rank (graph theory) 0101 mathematics Algebraically closed field Algebraic Geometry (math.AG) Discrete Mathematics and Combinatoric Mathematics Discrete mathematics Numerical Analysis Algebra and Number Theory Degree (graph theory) 010102 general mathematics Zero (complex analysis) Waring problem Mathematics - Commutative Algebra Rank Geometry and Topology 15A21 15A69 15A72 14A25 14N05 14N15 Ternary operation |
| Popis: | Let $\operatorname{r_{max}}(n,d)$ be the maximum Waring rank for the set of all homogeneous polynomials of degree $d>0$ in $n$ indeterminates with coefficients in an algebraically closed field of characteristic zero. To our knowledge, when $n,d\ge 3$, the value of $\operatorname{r_{max}}(n,d)$ is known only for $(n,d)=(3,3),(3,4),(3,5),(4,3)$. We prove that $\operatorname{r_{max}}(3,d)=d^2/4+O(d)$ as a consequence of the upper bound $\operatorname{r_{max}}(3,d)\le\left\lfloor\left(d^2+6d+1\right)/4\right\rfloor$. v1: 10 pages. v2: extended introduction and some mistakes corrected |
| Databáze: | OpenAIRE |
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