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SUMMARY:Jinyoung Park (Rutgers University)
DTSTART:20200511T130000Z
DTEND:20200511T140000Z
DTSTAMP:20260423T021037Z
UID:EPC/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/4/">The 
 number of maximal independent sets in the Hamming cube</a>\nby Jinyoung Pa
 rk (Rutgers University) as part of Extremal and probabilistic combinatoric
 s webinar\n\n\nAbstract\nLet $Q_n$ be the $n$-dimensional Hamming cube (hy
 percube) and $N = 2^n$. We prove that the number of maximal independent se
 ts in $Q_n$ is asymptotically $2n2^{N/4}$\, as was conjectured by Ilinca a
 nd Kahn in connection with a question of Duffus\, Frankl and Rödl. The va
 lue is a natural lower bound derived from a connection between maximal ind
 ependent sets and induced matchings. The proof of the upper bound draws on
  various tools\, among them “stability” results for maximal independen
 t set counts and old and new results on isoperimetric behavior in $Q_n$. T
 his is joint with Jeff Kahn.\n
LOCATION:https://researchseminars.org/talk/EPC/4/
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