Year: 2026
Type: preprint
Abstract: We prove an $Ω(n^2)$ lower bound on the determinantal complexity of the power sum polynomial $\sum_{i=1}^n x_i^n$ over the field of complex numbers. A similar result was claimed in a recent paper of Sheshadri (arXiv:2606.13628), via an AI-assisted and AI-written proof. Assuming its correctness, this was the first super-linear lower bound for this fundamental algebraic problem for any explicit polynomial. However, the authors of this note were unable to follow the details and verify the argument in arXiv:2606.13628, in spite of considerable effort on their part. The proof we provide here is short, (almost) self-contained and seemingly simpler.
Source: arXiv (Cornell University)
Authors: Kumar, Mrinal, Volk, Ben Lee
Institutions: Tata Institute of Fundamental Research, Reichman University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214755385