M.
Wachs 11: 00  11:50 Posets of partitions,
graphs and trees
We discuss some remarkable connections between the
homology of four different simplicial complexes, which have
arisen in various contexts. The first of these is the order complex
of a generalization of the partition lattice, namely the poset of
partitions of a finite set whose block sizes are congruent to 1 mod k,
for some fixed k. The second is the complex of graphs that don't
contain a perfect matching; the third is the complex of
graphs that are not kedge connected; and the fourth
is Hanlon's generalization
of the complex of homeomorphically irreducibe trees.
We give equivariant versions of results of
LinussonShareshianWelker and Jonsson relating the
homology of the odd block size partition poset to the
nonperfect matching complex and the not 2edge connected graph
complex. Our proofs rely on the construction of an
interesting basis for homology of the 1 mod k partition
poset, which
generalizes the wellknown nbc basis of Bj\"orner for the
homology of
the partition lattice.
This is joint work with John Shareshian
