The purpose of this paper is to compute the Möbius function of filters in the partition lattice formed by restricting to partitions by type. The Möbius function is determined in terms of the descent set statistics on permutations and the Möbius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Möbius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.
|Number of pages||10|
|Journal||Advances in Applied Mathematics|
|State||Published - Sep 2007|
Bibliographical noteFunding Information:
* Corresponding author. E-mail address: firstname.lastname@example.org (R. Ehrenborg). 1 Partially supported by National Science Foundation grant 0200624.
- Descent set statistic
- Euler and tangent numbers
- Knapsack partitions
- Set partition lattice
- r-Divisible partition lattice
ASJC Scopus subject areas
- Applied Mathematics