Particle statistics in three dimensions

A generalized framework for particle statistics is developed within which it becomes clear how bosons can combine to form fermions without violating the normal connection between spin and statistics. In the situation where internal and external particle degrees of freedom are separable, the possible statistical types are found and their combining rules derived. Here the statistical "interaction" between two particles is characterized either by the familiar sign or by an integer ("twist number"). However, further possibilities arise if the separability of external from internal degrees of freedom fails, as it can in gauge theories. In spatial dimensions other than three the "fermion from boson" phenomenon does not occur.