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

THE HOMOLOGY REPRESENTATIONS OF THE k-EQUAL PARTITION LATTICE

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 {1, 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 she...

THE HOMOLOGY REPRESENTATIONS OF THEk - EQUAL PARTITION

Symmetries of the k - bounded partition lattice

We generalize the symmetry on Young’s lattice, found by Suter, to a symmetry on the k-bounded partition lattice of Lapointe, Lascoux and Morse. Résumé. Nous généralisons la symmetrie sur le treillis de Young, découvert par Suter, à une symétrie sur le treillis des partages bornés par k et étudié par Lapointe, Lascoux and Morse.

A basis for the non-crossing partition lattice top homology

We find a basis for the top homology of the non-crossing partition lattice Tn . Though Tn is not a geometric lattice, we are able to adapt techniques of Björner (A. Björner, On the homology of geometric lattices. Algebra Universalis 14 (1982), no. 1, 107–128) to find a basis with Cn−1 elements that are in bijection with binary trees. Then we analyze the action of the dihedral group on this basis.

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چکیده ندارد.