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Graduate Student Combinatorics Seminar Sponsored by DIMACS

A spectral proof of Katona's t-intersection theorem

Aditya Potukuchi - Rutgers University

Location:  GSL - Hill 701
Date & time: Wednesday, 18 September 2019 at 12:15PM - 1:15PM

Abstract: Katona's theorem stated that a maximal t-intersecting family has size at most binom{n}{geq (n+t)/2}. The proof is by a tricky shifting argument. We will see a Fourier proof of the same result. This proof is somewhat easy (as easy as this type of proof can get I guess), and it possibly has its own merits. The reference I will be using is the following: https://anuragbishnoi.wordpress.com/2019/07/27/spectral-proofs-of-theorems-on-the-boolean-hypercube/