Möbius function on cross-section lattices.
The Möbius function \(\mu\) on partially ordered sets is an important enumerative and structural invariant in combinatorics. Two classical examples are particularly relevant to reductive (algebraic) monoids. First the Möbius function on the face lattice of a polytope is given by \(\mu(e,f)=(-1)^{l[e,f]}\), where \(l[e,f]\) denotes the length of the interval \([e,f]\). Second the Möbius function on a direct product of linear chains, given by \(\mu(e,f)=\begin{cases} (-1)^{l[e,f]},&\text{if }[e,f]\) is a Boolean lattice
scientific article; zbMATH DE number 2082024
scientific article