All reports by Author Chao Yan:

__
TR24-092
| 16th May 2024
__

Alexander Golovnev, Zeyu Guo, Pooya Hatami, Satyajeet Nagargoje, Chao Yan#### Hilbert Functions and Low-Degree Randomness Extractors

Alexander Golovnev, Zeyu Guo, Pooya Hatami, Satyajeet Nagargoje, Chao Yan

For $S\subseteq \mathbb{F}^n$, consider the linear space of restrictions of degree-$d$ polynomials to $S$. The Hilbert function of $S$, denoted $\mathrm{h}_S(d,\mathbb{F})$, is the dimension of this space. We obtain a tight lower bound on the smallest value of the Hilbert function of subsets $S$ of arbitrary finite grids in $\mathbb{F}^n$ ... more >>>