...d for each i. This yields S'= T'n. Thus if no two consecutive entries on the main diagonal are specified as 1's then S'= T'n. To complete the proof we need the standard result (for instance see Niven =-=[1]-=-) that the number of sequences of n plus and minus signs with no two minus signs adjacent is Fn+2. Incidence subgroups are themselves an interesting topic. The term comes from incidence algebra as use...