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Monotone Boolean functions capture their primes

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Abstract

It is shown that monotone Boolean functions on the Boolean cube capture the expected number of primes, under the usual identification by binary expansion. This answers a question posed by G. Kalai.

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Authors and Affiliations

  1. Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540, USA

    Jean Bourgain

Authors
  1. Jean Bourgain
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Corresponding author

Correspondence to Jean Bourgain.

Additional information

The research was partially supported by NSF grants DMS-0808042 and DMS-0835373.

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Bourgain, J. Monotone Boolean functions capture their primes. JAMA 124, 297–307 (2014). https://doi.org/10.1007/s11854-014-0033-6

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  • DOI: https://doi.org/10.1007/s11854-014-0033-6

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