Enumerating the Derangements of an n-Cube via Möbius Inversion
Bailey, Colin · Oliveira, Joseph
Original · EN
In L, the semilattice of faces of an n-cube, we count the number of automorphisms of 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.
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