The homology representations of the $k$-equal partition lattice
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- by Sheila Sundaram and Michelle Wachs PDF
- Trans. Amer. Math. Soc. 349 (1997), 935-954 Request permission
Abstract:
We determine the character of the action of the symmetric group on the homology of the induced subposet of the lattice of partitions of the set $\{1,2,\ldots ,n\}$ obtained by restricting block sizes to the set $\{1,k,k+1,\ldots \}$. 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 Björner and Wachs, with symmetric function techniques, developed by Sundaram, for determining representations on the homology of subposets of the partition lattice.References
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Additional Information
- Sheila Sundaram
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459; Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124
- Email: sheila@claude.math.wesleyan.edu
- Michelle Wachs
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- MR Author ID: 179695
- Email: wachs@math.miami.edu
- Received by editor(s): April 20, 1994
- Additional Notes: Supported in part by NSF grants DMS 9102760 and DMS 9311805
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 935-954
- MSC (1991): Primary 05E25, 06A08, 06A09; Secondary 05E05, 05E10, 20C30, 05A18, 52B30
- DOI: https://doi.org/10.1090/S0002-9947-97-01806-0
- MathSciNet review: 1389790