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

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

2009-02-05

arxiv.org/abs/0902.0937v2

Mathematics

Combinatorics

13 pages, minor revisions of definitions

Scientific paper

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 M\"obius inversion we get a formula for
the number of derangements on the $n$-cube in terms of the M\"obius function on
the lattice of MR-subalgebras. We compute this M\"obius function.

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