Problems
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If Y = Y_{r_1} \cup Y_{r_2} is a tight relative 3-design in H(n, 2) with constant weight and r_1 + r_2 = n, then is it true that the corresponding designs (V, \mathcal{B}{r_1}) and (V, \mathcal{B}{r_2}) are necessarily complement with each…
In view of the absence of the Shannon effect and Kozik’s result on the limiting distributions it seems reasonable that asymptotically almost all functions have polynomial complexity.
We believe that equality should hold in Theorem 1.
We close this paper with the following conjecture: all r-dimensional grids, with finitely many exceptions, are domatically full.
Suppose 17/30≤α≤1 and β>(2 α-1)/4 or 43/120≤α<17/30 and β>(5 α-2)/25 . For all sufficiently large n, a graph of order n in which each set of ⌊α n⌋ vertices spans at least β n^2 edges must contain a triangle.
independence_number(x)>= ceil(lovasz_theta(x))-girth(x)
For n≥2 B(K_2,n,Z_2n)≤4n-3 .