Influences of monotone Boolean functions
Demetres Christofides
TL;DR
This paper proves Keller and Pilpel's conjecture that the influence of a monotone Boolean function remains unchanged under invertible linear transformations.
Contribution
It provides a proof confirming that the influence of monotone Boolean functions is invariant under invertible linear transformations.
Findings
Influence remains unchanged under invertible linear transformations.
Confirms Keller and Pilpel's conjecture.
Advances understanding of Boolean function properties.
Abstract
Recently, Keller and Pilpel conjectured that the influence of a monotone Boolean function does not decrease if we apply to it an invertible linear transformation. Our aim in this short note is to prove this conjecture.
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Taxonomy
TopicsAdvanced Algebra and Logic