Towards understanding the probability of 0+ ground states in even-even many-body systems

For single-j shells with j=7/2, 9/2, and 11/2, we relate the large probability of I⁺ ground states to the largest (smallest) coefficients α^J_I(vβ)=<nvβI\|A^J†.A^J\|nvβI>, where n is the particle number, v is the seniority, β is an additional quantum number, and I is the angular momentum of the state. Interesting regularities of the probabilities of I⁺ ground states are noticed and discussed for four-particle systems. Several counter examples of the 0⁺ ground state (0g.s.) predominance are noticed for the first time.