The Möbius number of the symmetric group
Date
2012
Authors
Monks, Kenneth M., author
Hulpke, Alexander, advisor
Penttila, Tim, committee member
Achter, Jeff, committee member
Toki, Walter, committee member
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Abstract
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.
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Subject
combinatorics
symmetric group
Möbius
group theory