On computing boundary functional sums

AbstractA method for solving enumeration problems is suggested. We consider the enumeration problems which are reducible to estimation of the sums of type T(X,f)=ΣAf(A) where f is so called boundary functional (BF) on X, and the summation is over all subsets of X (or over some special subfamily of 2X). An evolution of the n-cube, the percolation problem, the problem of computation of the matchings number and the independent sets number, the monotone Boolean functions number, the binary codes number and so on are among such problems. We show how to obtain asymptotics for T(X,f). In conclusion we give an example of application of the BF method to finding the number of independent sets in the bipartite graphs, induced by neighbouring levels of the n-cube

On Approximation of Stepfunctions

this paper is to specify the set of all solutions of these minimization problems. We prove the following statements. Theorem 1 It holds