Filter-regular sequences, almost complete intersections and Stanley's conjecture

Let $K$ be a field and $I$ a monomial ideal of the polynomial ring $S=K[x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n]$ generated by monomials $u_1,u_2,\mathrm{.}\mathrm{.}\mathrm{.},u_t$. We show that $S\mathrm{/}I$ is pretty clean if either: 1) $u_1,u_2,\mathrm{.}\mathrm{.}\mathrm{.},u_t$ is a filter-regular sequence, 2) $u_1,u_2,\mathrm{.}\mathrm{.}\mathrm{.},u_t$ is a $d$-sequence; or 3) $I$ is almost complete intersection. In particular, in each of these cases, $S\mathrm{/}I$ is sequentially Cohen-Macaulay and both Stanley’s and $h$-regularity conjectures, on Stanley decompositions, hold for $S\mathrm{/}I$. Also, we prove that if $I$ is the Stanley-Reisner ideal of a locally complete intersection simplicial complex on $[n]$, then Stanley’s conjecture holds for $S\mathrm{/}I$.