Combinatorial interpretation of Kolmogorov complexity

The very first Kolmogorov´s paper on algorithmic information theory was entitled “Three approaches to the definition of the quantity of information”. These three approaches were called combinatorial, probabilistic and algorithmic. Trying to establish formal connections between combinatorial and algorithmic approaches, we prove that every linear inequality including Kolmogorov complexities could be translated into an equivalent combinatorial statement. Entropy (complexity) proofs of combinatorial inequalities given previously can be considered as a special case (and a natural starting points) for this translation