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SUMMARY:Jinyoung Park (Rutgers University)
DTSTART:20200511T130000Z
DTEND:20200511T140000Z
DTSTAMP:20260404T143403Z
UID:EPC/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EPC/4
 /">The number of maximal independent sets in the Hamming cube</a>\nby Jiny
 oung Park (Rutgers University) as part of Extremal and probabilistic combi
 natorics webinar\n\n\nAbstract\nLet $Q_n$ be the $n$-dimensional Hamming c
 ube (hypercube) and $N = 2^n$. We prove that the number of maximal indepen
 dent sets in $Q_n$ is asymptotically $2n2^{N/4}$\, as was conjectured by I
 linca and Kahn in connection with a question of Duffus\, Frankl and Rödl.
  The value is a natural lower bound derived from a connection between maxi
 mal independent sets and induced matchings. The proof of the upper bound d
 raws on various tools\, among them “stability” results for maximal ind
 ependent set counts and old and new results on isoperimetric behavior in $
 Q_n$. This is joint with Jeff Kahn.\n
LOCATION:https://stable.researchseminars.org/talk/EPC/4/
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