90 citations · 333 across the 51 of their papers we have counts for
4 papers · 1 filter
Ranks of tensors and a generalization of secant varieties
Jarosław Buczyński, J. M. Landsberg
We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partia…
Holographic algorithms without matchgates
J. M. Landsberg, Jason Morton, Serguei Norine
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In…
Kruskal's theorem
J. M. Landsberg
This is just a short proof of Kruskal's theorem regarding uniqueness of expressions for tensors, phrased in geometric language.
On the ranks and border ranks of symmetric tensors
J. M. Landsberg, Zach Teitler
Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We…