Some Combinatorial Aspects of Composition of a Set of Functions

Additionally, we make an assumption that Ai are non-empty sets, for i=0, 1, . . . ,m, where m=[n/2]. For each set of functions An we determine the number of meaningful compositions of higher order in implicit and explicit form. Let us define a binary relation ρ ”to be in composition” with ∇iρ∇j = 1 iff the composition ∇j ◦∇i is meaningful for i, j ∈ {1, 2, . . . , n}. Let us form an adjacency matrix A = [aij ] of the graph, determined by relation ρ, with