The number of possible multilateral relations among iuris gentium subjects and the mathematical formula determining treaty-making-power of single subject

The purpose of this text is to conduct the mathematical analysis in order to find formula, which allows to determine the number of all non-repeatable relations (starting from bilateral, through plurilateral, ending on multilateral - universal treaty), which may be potentially constructed by defined number of subjects of international law. Additionally the authors described "treaty-making-power" of single subject: number of group relations in which the subject could participate. The authors pointed out that states do not use even small part of their treaty making possibilities.