Extending Higher Bruhat Orders to Non-longest Words in S_n
| dc.contributor.advisor | Elias, Ben | |
| dc.contributor.author | Hothem, Daniel | |
| dc.date.accessioned | 2021-09-13T18:34:37Z | |
| dc.date.available | 2021-09-13T18:34:37Z | |
| dc.date.issued | 2021-09-13 | |
| dc.description.abstract | In this paper, we extend Manin and Schechtman's higher Bruhat orders for the symmetric group to higher Bruhat orders for non-longest words w in the symmetric group. We prove that the higher Bruhat orders of non-longest words are ranked posets with unique minimal and maximal elements. As in Manin and Schechtman's original paper, the k-th Bruhat order for w is created out of equivalence classes of maximal chains in its (k-1)-st Bruhat order. We also define the second and third Bruhat orders for arbitrary realizable k-sets, and prove that the second Bruhat order has a unique minimal and maximal element. Lastly, we also outline how this extension may guide future research into developing higher Bruhat orders for affine type A Weyl groups. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/26617 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | Bruhat order | en_US |
| dc.subject | Symmetric Group | en_US |
| dc.title | Extending Higher Bruhat Orders to Non-longest Words in S_n | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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