On a quotient topology of the partition lattice with forbidden block sizes (Q411799)
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scientific article; zbMATH DE number 6029109
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a quotient topology of the partition lattice with forbidden block sizes |
scientific article; zbMATH DE number 6029109 |
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On a quotient topology of the partition lattice with forbidden block sizes (English)
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30 April 2012
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The partitions of the set \(\{1,2,\dots,n\}\) are partially ordered by refinement. This poset forms a lattice which admits a natural action of the symmetric group \(S_n\). The author determines the homotopy types of quotients of certain sub-posets by the induced action of the stabilizer (in \(S_n\)) of a fixed number \(k\in\{1,2,\dots,n\}\). Moreover, bases for the cohomology rings are given. The proofs employ techniques from discrete Morse theory.
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discrete Morse theory
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