  Let $I\supsetneq J$ be two square free monomial ideals of a polynomial
algebra over a field generated in degree $\geq 1$, resp. $\geq 2$ . Almost
always when $I$ contains precisely one variable, the other generators having
degrees $\geq 2$, if the Stanley depth of $I/J$ is $\leq 2$ then the usual
depth of $I/J$ is $\leq 2$ too, that is the Stanley Conjecture holds in these
cases.
