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- W2912044029 abstract "Komlos conjecture is about the existing of a universal constant K such that for all dimension n and any collection of vectors (V_1 ) ⃗ ,…,(V_n ) ⃗ ∈R^n with ‖(V_i ) ⃗ ‖_2≤1 , there are weights ε_i∈{-1,1} in such that ‖∑_(i=1)^n▒〖ϵ_i (V_i ) ⃗ 〗‖_∞≤K(n)≤K. In this paper, the constant K(n) is evaluated for n≤5 to be K(2)=√2, K(3)=(√2+√11)/3, K(4)=√3, and K(5)=(4+√142)/9. For higher dimension, the function f(n)=√(n-⌈〖 log〗_2 (2^(n-1)⁄n)⌉ ) is found to be the lower bound for the constant K(n), from where it can be concluded that the Komlos conjecture is false i.e., the universal constant K=max┬(‖(V_i ) ⃗^* ‖_2≤1)min┬(ε_i=±1)〖‖∑_(i=1)^n▒〖ϵ_i (V_i ) ⃗^* 〗‖_∞ 〗 does not exsit because of lim┬(n→∞)〖K(n)≥lim┬(n→∞)√(log(n)-1)=+∞〗." @default.
- W2912044029 created "2019-02-21" @default.
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- W2912044029 date "2019-02-06" @default.
- W2912044029 modified "2023-09-26" @default.
- W2912044029 title "The Disprove of the Komlos Conjecture" @default.
- W2912044029 cites W1518816409 @default.
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- W2912044029 doi "https://doi.org/10.20944/preprints201902.0059.v1" @default.
- W2912044029 hasPublicationYear "2019" @default.
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