The Deletion Order and Coxeter Groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915165760389120 |
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| author | Nicolaides, Robert Rowley, Peter |
| author_facet | Nicolaides, Robert Rowley, Peter |
| contents | The deletion order of a finitely generated Coxeter group W is a total order on the elements which, as is proved, is a refinement of the Bruhat order. This order is applied in [8] to construct Elnitsky tilings for any finite Coxeter group. Employing the deletion order, a corresponding normal form of an element w of W is defined which is shown to be the same as the normal form of w using right to left lexicographic ordering. Further results on the deletion order are obtained relating to the property of being Artinian and, when W is finite, its interplay with the longest element of W. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_07881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Deletion Order and Coxeter Groups Nicolaides, Robert Rowley, Peter Group Theory Combinatorics The deletion order of a finitely generated Coxeter group W is a total order on the elements which, as is proved, is a refinement of the Bruhat order. This order is applied in [8] to construct Elnitsky tilings for any finite Coxeter group. Employing the deletion order, a corresponding normal form of an element w of W is defined which is shown to be the same as the normal form of w using right to left lexicographic ordering. Further results on the deletion order are obtained relating to the property of being Artinian and, when W is finite, its interplay with the longest element of W. |
| title | The Deletion Order and Coxeter Groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2407.07881 |