Permanental compounds and permanents of (0, 1)-circulants

AbstractIt was shown by the author in a recent paper that a recurrence relation for permanents of (0, 1)-circulants can be generated from the product of the characteristic polynomials of permanental compounds of the companion matrix of a polynomial associated with (0, 1)-circulants of the given type. In the present paper general properties of permanental compounds of companion matrices are studied, and in particular of convertible companion matrices, i.e., matrices whose permanental compounds are equal to the determinantal compounds after changing the signs of some of their entries. These results are used to obtain formulas for the limit of the nth root of the permanent of the n × n (0, 1)-circulant of a given type, as n tends to infinity. The root-squaring method is then used to evaluate this limit for a wide range of circulant types whose associated polynomials have convertible companion matrices