Homotopy Type of Intervals of the Second Higher Bruhat Orders
The higher Bruhat order is a poset generalizing the weak order on permutations. Another special case of this poset is an ordering on simple wiring diagrams. For this case, we prove that every interval is either contractible or homotopy equivalent to a sphere. This partially proves a conjecture due t...
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2018
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| Online Access: | http://hdl.handle.net/1721.1/119674 https://orcid.org/0000-0001-9276-4291 |
| Summary: | The higher Bruhat order is a poset generalizing the weak order on permutations. Another special case of this poset is an ordering on simple wiring diagrams. For this case, we prove that every interval is either contractible or homotopy equivalent to a sphere. This partially proves a conjecture due to Reiner. Our proof uses some tools developed by Felsner and Weil to study wiring diagrams. Keywords: Higher Bruhat, Order complex, Mobius function, Wiring diagram, Rhombic tiling |
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