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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.15093 |
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| _version_ | 1866909621461975040 |
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| author | Bingham, Aram Morera, Néstor Díaz |
| author_facet | Bingham, Aram Morera, Néstor Díaz |
| contents | In this paper, we show that the Bruhat order on any sect of a symmetric variety of type $AIII$ is lexicographically shellable. Our proof proceeds from a description of these posets as rook placements in a partition shape which fits in a $p \times q$ rectangle. This allows us to extend an EL-labeling of the rook monoid given by Can to an arbitrary sect. As a special case, our result implies that the Bruhat order on matrix Schubert varieties is lexicographically shellable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15093 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lexicographic shellability of sects Bingham, Aram Morera, Néstor Díaz Combinatorics 05E14 In this paper, we show that the Bruhat order on any sect of a symmetric variety of type $AIII$ is lexicographically shellable. Our proof proceeds from a description of these posets as rook placements in a partition shape which fits in a $p \times q$ rectangle. This allows us to extend an EL-labeling of the rook monoid given by Can to an arbitrary sect. As a special case, our result implies that the Bruhat order on matrix Schubert varieties is lexicographically shellable. |
| title | Lexicographic shellability of sects |
| topic | Combinatorics 05E14 |
| url | https://arxiv.org/abs/2312.15093 |