Enumerating the Derangements of an $n$-Cube via Möbius Inversion

Abstract

In $\mathcal{L}$, the semilattice of faces of an $n$-cube, we count the number of automorphisms of $\mathcal{L}$ that fix a given subalgebra -- either pointwise or as a subalgebra. By using Möbius inversion we get a formula for the number of derangements on the $n$-cube in terms of the Möbius function on the lattice of MR-subalgebras. We compute this Möbius function.

13 pages, minor revisions of definitions

References in corpus (1)

• The Möbius Function on Implication sublattices of a Boolean algebra