Sep 5, 2020 · Our result is the first lower bound for any explicit polynomial which is bigger by a constant factor than \max\{n,d\}, and improves upon the ...
Sep 19, 2022 · For every n-variate polynomial of degree d, the determinantal complexity is trivially at least d, and it is a long-standing open problem to ...
Due to the completeness property mentioned above, a lower bound of s on the determinantal complexity of f will imply the same lower bound for algebraic formulas ...
For every n-variate polynomial of degree d, the determinantal complexity is trivially at least d, and it is a long standing open problem to prove a lower bound ...
For every n-variate polynomial of degree d, the determinantal complexity is trivially at least d, and it is a long standing open problem to prove a lower bound ...
Jul 8, 2021 · Our result is the first lower bound for any explicit polynomial which is bigger by a constant factor than max{n,d}, and improves upon the prior ...
This work proves that the determinantal complexity of the polynomial $\sum_{i = 1}^n x_i^n$ is at least $1.5n - 3$ and improves upon the prior best bound of ...
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Sep 29, 2021 · Our result is the first lower bound for any explicit polynomial which is bigger by a constant factor than max{n, d}, and improves upon the prior best bound of ...
In this section, we prove the best lower bound for the determinantal complexity, due to Mignon and Ressayre [MR04]. 1.1.1 Observation. ∂. ∂Xi,j pern(X) is ...
We prove that the determinantal complexity of a hypersurface of degree $d > 2$ is bounded below by one more than the codimension of the singular locus, ...