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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The homology representations of the
$k$-equal partition lattice


Authors: Sheila Sundaram and Michelle Wachs
Journal: Trans. Amer. Math. Soc. 349 (1997), 935-954
MSC (1991): Primary 05E25, 06A08, 06A09; Secondary 05E05, 05E10, 20C30, 05A18, 52B30
MathSciNet review: 1389790
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Abstract | References | Similar Articles | Additional Information

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.


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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
Email: wachs@math.miami.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01806-0
PII: S 0002-9947(97)01806-0
Received by editor(s): April 20, 1994
Additional Notes: Supported in part by NSF grants DMS 9102760 and DMS 9311805
Article copyright: © Copyright 1997 American Mathematical Society