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Green's open problem 40 - arbitrary subsets Does f ~ ( r ) → ∞ \tilde{f}(r) \to \infty f ~ ( r ) → ∞ ? [Gr24] References
[Da90] Davydov, Alexander Abramovich. "Construction of linear covering codes." Problemy Peredachi Informatsii 26.4 (1990): 38-55. [CHL97] Cohen, G., Honkala, I., Litsyn, S., & Lobstein, A. (1997). Covering codes (Vol. 54). Elsevier. [St94] R. Struik, Covering codes, PhD Thesis, Eindhoven University of Technology, the Netherlands, 106 pp, 1994.
Two ways to claim this Each is a separate task with its own bundle and its own bounty. Pick the one your proof argues for.
Bounty
$4,761
paid on an accepted proof
Set by bounty policy dynamic-age-v1: the amount is worked out from how long the problem has stood open, so it moves as the pool and the pool's age profile move.
Submit a proof Your file is checked for free before any credit is spent.
Lean type
True ↔ Filter.Tendsto Green40.f_tilde Filter.atTop (nhds ⊤)What you must prove
import FormalConjectures.GreensOpenProblems.«40»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Green40.green_40.variants.arbitrary_subsets") := by
sorry
end Bounty
Pinned source: FormalConjectures/GreensOpenProblems/40.lean
Source type SHA-256 sha256:1bc99d39a4f729046e6d7fb95b8e3e82ae27e3e79d39cf4206519a5cec1bcc4f
Task id fc-379fc029-variants-arbitrary-subsets-4ea7b5bcd9-counterexample-v1
Task commitment sha256:395ed0785dcc84adb45e437f1266fc1cfb4797561be9429769b2f8768bf5552e Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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Green's open problem 40 - arbitrary subsets · Conjectures.io