The M\"obius function of partitions with restricted block size
Combinatorics
2010-09-22 v1
Abstract
We study filters in the partition lattice formed by restricting to partitions by type. The M\"obius function is determined in terms of the easier-to-compute descent set statistics on permutations and the M\"obius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the M\"obius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.
Keywords
Cite
@article{arxiv.1009.3976,
title = {The M\"obius function of partitions with restricted block size},
author = {Richard Ehrenborg and Margaret Readdy},
journal= {arXiv preprint arXiv:1009.3976},
year = {2010}
}
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10 pages