Name
Abstract | ||
|---|---|---|
Methods from numerical algebraic geometry are applied in combination with techniques from classical representation theory to show that the variety of 3 x 3 x 4 tensors of border rank 4 is cut out by polynomials of degree 6 and 9. Combined with results of Landsberg and Manivel, this furnishes a computational solution of an open problem in algebraic statistics, namely, the set-theoretic version of Allman's salmon conjecture for 4 x 4 x 4 tensors of border rank 4. A proof without numerical computation was given recently by Friedland and Gross. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1080/10586458.2011.576539 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
Salmon conjecture,algebraic statistics,representation theory,numerical algebraic geometry,Bertini | Discrete mathematics,Topology,Open problem,Tensor,Polynomial,Mathematical analysis,Numerical algebraic geometry,Representation theory,Conjecture,Algebraic statistics,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
20.0 | 3.0 | 1058-6458 |
Citations | PageRank | References |
3 | 0.54 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel J. Bates | 1 | 103 | 12.03 |
| Luke Oeding | 2 | 34 | 4.57 |