| In the recent papers [1], [2], we showed that the M?bius inversion can be generalized to the locally infinite, point-representable poset. The point of the present paper is to exploit *-inite structures in the study of combinatorics. It is noted that there exists some locally *-inite poset C containing all the standard entities in the natural extension *S of a locally infinite poset S, and then a *-ncidence algebra. *I(C,*K) of C, over a field *K of characteristic 0, is defined. It follows from this that the M?bius inversion can be generalized to general locally *-finite posets. An application to some linearly ordered set is given anew of such result. |
