M\"obius numbers of some modified generalized noncrossing partitions

In this paper we will give a M"obius number of $NC^{k}(W) \setminus \bf{mins} \cup {\hat{0} }$foraCoxetergroup$W$ which contains an affirmative answer for the conjecture 3.7.9 in Armstrong’s paper [ Generalized noncrossing partitions and combinatorics of Coxeter groups. arXiv:math/0611106].