Boolean functions [See also 94D10]
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Fourier Entropy-Influence constant: determine C 71 or improve its bounds; the repository records 6.278 (6.521845710923046575 ) (lower) and infty (upper).
Maximal number of relevant variables in Boolean functions of degree d : determine C 44 or improve its bounds; the repository records 1.5 (lower) and 4.394 (upper).
The degree--sensitivity exponent: determine C 37 or improve its bounds; the repository records log 3 (6) approx 1.63093 (lower) and 2 (upper).
Bohnenblust--Hille constant on the Boolean cube: determine C 26a or improve its bounds; the repository records 2 (lower) and infty (upper).
Critical exponent for isoperimetric inequality on the Hamming cube: determine C 11b or improve its bounds; the repository records 0.5 (lower) and 0.5 (upper).
L^1 Poincaré constant on the Hamming cube: determine C 11a or improve its bounds; the repository records sqrt pi/2 approx 1.2533 (lower) and pi/2 - 0.00013 approx 1.5707 (upper).
Sensitivity versus Degree for Boolean Multilinear Polynomials. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.
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Springer Nature / Birkhäuser
Order, lattices and universal algebra
2023 · 8 questions extracted
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