On boundaries and influences

Abstract

We prove an inequality relating the size of the boundary of a monotone subset of {0,1}n and the influences of the coordinates upon this set. It shows that if the boundary (resp. the influences) are small, the influences (resp. the boundary) are large.

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Work partially supported by an NSF grant.

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Talagrand, M. On boundaries and influences. Combinatorica 17, 275–285 (1997). https://doi.org/10.1007/BF01200910

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Mathematics Subject Classification (1991)

  • 05D05
  • 06E30