#### Volume 4, issue 2 (2004)

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Partition complexes, duality and integral tree representations

### Alan Robinson

Algebraic & Geometric Topology 4 (2004) 943–960
 arXiv: math.CT/0410555
##### Abstract

We show that the poset of non-trivial partitions of $\left\{1,2,\dots ,n\right\}$ 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 ${\Sigma }_{n}$ and ${\Sigma }_{n+1}$ on the homology and cohomology of this partially-ordered set.

##### Keywords
partition complex, Lie superalgebra
##### Mathematical Subject Classification 2000
Primary: 05E25
Secondary: 17B60, 55P91