The Homology of Partitions with an Even Number of Blocks

@inproceedings{Sundaram1996TheHO,
  title={The Homology of Partitions with an Even Number of Blocks},
  author={Sheila Sundaram},
  year={1996}
}
Let Pe2n denote the subposet obtained by selecting even ranks in the partition lattice P2n. We show that the homology of Pe2n has dimension (2n)! E2n-1, where E2n-1 is the tangent number. It is thus an integral multiple of both the Genocchi number and an Andre or simsun number. Using the general theory of rankselected homology representations developed in [22], we show that, for the special case of Pe2n, the character of the symmetric group S2n on the homology is supported on the set of… CONTINUE READING