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.identifier.uri |
https://scholarsbank.uoregon.edu/xmlui/handle/1794/26617 |
|
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.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.name |
Ph.D. |
|
thesis.degree.level |
doctoral |
|
thesis.degree.discipline |
Department of Mathematics |
|
thesis.degree.grantor |
University of Oregon |
|