English

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}
}

Comments

10 pages

R2 v1 2026-06-21T16:16:36.746Z