The excitation functions of K^+ and K^- mesons in heavy ion collisions are studied within a statistical model assuming chemical and thermal equilibrium with exact strangeness conservation. At low incident energies the associate production of kaons, i.e. the production of a K+ together with a hyperon and the production of a K- together with a K+, implies specific features: different threshold energies and different dependences of K+ and K- yields on baryon number density. It is shown that the

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... erimentally observed equality of the K^+ and K^- rates at energies √(s) - √(s_th)≤ 0 is due to a crossing of the two excitation functions. Furthermore, the independence of the K^+ to K^- ratio on the number of participating nucleons observed at 1 and 10 A·GeV is consistent with this model.