On the Number of H-functions Depending on n Variables
by
Dimiter Stoichkov Kovachev
South-West-University Blagoevgrad

A discrete function f(x₁,  x₂, ..., x_n) depends on the variable x_i of kind H if for each set of values of the variables of f

c_i',  c_i'',  c₁, c₂, ... , c_i-1, c_i+1, ... , c_n   (c_i' =/= c_i'') it holds

f(c₁, ..., c_i-1, c_i', c_i+1, ... , c_n) =/= f(c₁, ..., c_i-1, c_i'', c_i+1, ... , c_n).

A function f(x₁,  x₂, ..., x_n) is called H-function if it depends of kind H on all its essential variables.

We prove that the number of all H-functions of n essential variables in k-valued logic is equal to the number of all Latin n-cubes over the set {1, 2, ... , k}.

Date received: May 13, 2004