THE HOMOLOGY REPRESENTATIONS OF THEk - EQUAL PARTITION
نویسندگان
چکیده
منابع مشابه
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...
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The primary aim of this paper is to illustrate the use of a well-known technique of algebraic topology, the Hopf trace formula, as a tool in computing homology representations of posets. Inspired by a recent paper of Bjj orner and Lovv asz ((BL]), we apply this tool to derive information about the homology representation of the symmetric group S n on a class of subposets of the partition lattic...
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We show that the poset of non-trivial partitions of {1, 2, . . . , n} has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups Σn and Σn+1 on the homology and cohomology of this partially-ordered set. AMS Classification 05E25; 17B60, 55P91
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We show that the poset of non-trivial partitions of {1, 2, . . . , n} has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups Σn and Σn+1 on the homology and cohomology of this partially-ordered set. AMS Classification 05E25; 17B60, 55P91
متن کاملMultiplicity of the Trivial Representation in Rank-selected Homology of the Partition Lattice
We study the multiplicity bS(n) of the trivial representation in the symmetric group representations βS on the (top) homology of the rankselected partition lattice ΠSn. We break the possible rank sets S into three cases: (1) 1 6∈ S, (2) S = 1, . . . , i for i ≥ 1 and (3) S = 1, . . . , i, j1, . . . , jl for i, l ≥ 1, j1 > i + 1. It was previously shown by Hanlon that bS(n) = 0 for S = 1, . . . ...
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تاریخ انتشار 1995