### 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,... ,n} obtained by restricting block sizes to the set {l, k, k + 1,... }. 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.

Original language | English (US) |
---|---|

Pages (from-to) | 935-954 |

Number of pages | 20 |

Journal | Transactions of the American Mathematical Society |

Volume | 349 |

Issue number | 3 |

State | Published - 1997 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*349*(3), 935-954.

**The homology representations of the k-equal partition lattice.** / Sundaram, Sheila; Galloway, Michelle L.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 349, no. 3, pp. 935-954.

}

TY - JOUR

T1 - The homology representations of the k-equal partition lattice

AU - Sundaram, Sheila

AU - Galloway, Michelle L

PY - 1997

Y1 - 1997

N2 - 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,... ,n} obtained by restricting block sizes to the set {l, k, k + 1,... }. 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.

AB - 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,... ,n} obtained by restricting block sizes to the set {l, k, k + 1,... }. 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.

UR - http://www.scopus.com/inward/record.url?scp=21744436373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21744436373&partnerID=8YFLogxK

M3 - Article

VL - 349

SP - 935

EP - 954

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -