Monotone Boolean functions capture their primes
Jean Bourgain
TL;DR
This paper demonstrates that monotone Boolean functions on the Boolean cube accurately represent the expected number of primes, addressing a question posed by G. Kalai.
Contribution
It establishes a connection between monotone Boolean functions and prime counting, providing a new perspective on prime distribution within Boolean functions.
Findings
Monotone Boolean functions capture the expected number of primes.
Answers a question posed by G. Kalai.
Provides a new approach to understanding primes through Boolean functions.
Abstract
It is shown that monotone Boolean functions on the Boolean cube capture the expected number of primes, under he usual identification by binary expansion. This answers a question posed by G.Kalai.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Advanced Combinatorial Mathematics