The border determinantal complexity of sum_{i=1}^n x_i^n is at least (n-1)^2/(4e) and the symmetric version at least (n-1)^2/(2e) for n>=3 over the complexes.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
cs.CC 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves sdc(sum x_i^n) >= (1/(2e) - o(1)) n^2 over C using polar degree of the associated hypersurface and multihomogeneous Bezout on an incidence variety after symmetric Schur complement.
citing papers explorer
-
A near-quadratic lower bound on the border determinantal complexity of $\sum_i x_i^n$ via conormal specialization
The border determinantal complexity of sum_{i=1}^n x_i^n is at least (n-1)^2/(4e) and the symmetric version at least (n-1)^2/(2e) for n>=3 over the complexes.
-
A symmetric determinantal lower bound for diagonal power sums via polar degree
Proves sdc(sum x_i^n) >= (1/(2e) - o(1)) n^2 over C using polar degree of the associated hypersurface and multihomogeneous Bezout on an incidence variety after symmetric Schur complement.