## THE HOMOLOGY REPRESENTATIONS OF THE
k-EQUAL PARTITION LATTICE

**
Sheila Sundaram and Michelle Wachs**
**Abstract:**
TWe determine the character of the action of the symmetric group on the homology
of the induced subposet of the lattice of partitions of $\{1,2,\dots,n\}$
obtained by restricting block sizes to the set $\{1,k,k+1,\dots\}$.
A plethystic formula for the generating function of the Frobenius characteristic
of the representation is given. We combine techniques from the theory of nonpure
shellability, recently developed by Bj\"orner and Wachs, with symmetric function
techniques, developed by Sundaram, for determining representations on the homology
of subposets of the partition lattice.

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