I have read in a paper that $\mu(0,1)\neq 0$, for the Möbius function $\mu$ on an atomistic (finite, modular) lattice with $0$ and $1$. Could someone provide me with a reference for this claim? Many thanks in advance.



Möbius function on atomistic (modular) lattices
More generally, the Möbius function of a geometric lattice is never 0. Although not stated explicitly in the text of *Enumerative Combinatorics*, vol. 1, 2nd ed., it is a simple consequence of equation (3.33) on page 277, as mentioned in the solution to Exercise 3.100(b). It also follows from Exercise 3.98 (where the displayed $\leq$ should be $\geq$) and from Exercise 3.99.


