In this paper, we partially confirm a conjecture, proposed by Cimpoeas,
Keller, Shen, Streib and Young, on the Stanley depth of squarefree Veronese
ideals $I_{n,d}$. They conjecture that, for positive integers $1 \le d \le n$,
$\sdepth (I_{n,d})= \lfloor \binom{n}{d+1}/\binom{n}{d} t\rfloor+d$. Herzog,
Vladoiu and Zheng established a connection between the Stanley depths of
quotients of monomial ideals and interval partitions of certain associated
partially ordered sets.