The Möbius number of the symmetric group - Monks, Kenneth M., author; Hulpke, Alexander, advisor; Penttila, Tim, committee member; Achter, Jeff, committee member; Toki, Walter, committee member (Colorado State University. Libraries, 2012)
The Möbius number of a finite group is its most important nontrivial combinatorial invariant. In this paper, we compute the Möbius numbers of many partially-ordered sets, including the odd-partition posets and the subgroup lattices of many infinite families of groups. This is done with an eye towards computing the Möbius number of the symmetric group on 18 points.
Keywords: combinatorics; symmetric group; Möbius; group theory