Asymptotics for the Logarithm of the Number of (k, l)-Solution-Free Collections in an Interval of Naturals

详细

A collection (A₁, … ,A_k+l) of subsets of an interval [1, n] of naturals is called (k, l)-solution-free if there is no set (a₁, … , a_k+l) ∈ A₁ × ⋯ × A_k+l that is a solution to the equation x₁ + ⋯ + x_k = x_k+1 + ⋯ + x_k+l. We obtain the asymptotics for the logarithm of the number of sets (k, l)-free of solutions in an interval [1, n] of naturals.