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Seminar Details

Covering the Hypercube with Hyperplanes

  • Start Date: March 12, 2025
  • Event Start Time: 12:15 PM
  • Event End Time: 1:15 PM
  • Seminar Series: Graduate Combinatorics Seminar
  • Presenter(s): Caleb Fong - Rutgers University
  • Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
  • Event Additional Info: <p>See:&nbsp;<a href="https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html">https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html</a></p>
  • Presentation Type: Stand Alone Presentation
  • Abstract:

    The n-dimensional Boolean hypercube Q_n can be easily covered with 2 hyperplanes. If you add the additional restriction that exactly one point must remain uncovered, it takes some work to show—as Alon and Furedi did in 1993—that you need at least n hyperplanes to cover the rest. We will see the quick Combinatorial Nullstellensatz proof of this result, along with some more recent work on k-fold hyperplane covers of the hypercube (minus a point) due to Alexander Clifton and Hao Huang in 2019.