We show that the poset of non-trivial partitions of has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups and on the homology and cohomology of this partially-ordered set.
"Partition complexes, duality and integral tree representations." Algebr. Geom. Topol. 4 (2) 943 - 960, 2004. https://doi.org/10.2140/agt.2004.4.943