Characterizations of {1,3}-Bohemian inverses of structured matrices

This paper presents {1,3}-Bohemian inverses of a certain type of structured {-1,0,1}-matrices, particularly full and well-settled matrices. It begins by characterizing the rank-one Bohemian matrices for the population P = {-1,0,1}. Characterizations of the {3} and {1,3}-Bohemian inverses are presented for arbitrary population over the set {-1,0,1}. Furthermore, explicit formulas are provided to enumerate the {1, 3}-Bohemian inverses of these matrices when the population is exactly {-1,0,1}. Moreover, corresponding results for {3}-inverses are obtained.