English

Slicing the hypercube is not easy

Combinatorics 2021-02-18 v2 Artificial Intelligence Computational Complexity

Abstract

We prove that at least Ω(n0.51)\Omega(n^{0.51}) hyperplanes are needed to slice all edges of the nn-dimensional hypercube. We provide a couple of applications: lower bounds on the computational complexity of parity, and a lower bound on the cover number of the hypercube by skew hyperplanes.

Keywords

Cite

@article{arxiv.2102.05536,
  title  = {Slicing the hypercube is not easy},
  author = {Gal Yehuda and Amir Yehudayoff},
  journal= {arXiv preprint arXiv:2102.05536},
  year   = {2021}
}

Comments

20 pages

R2 v1 2026-06-23T23:02:15.633Z