Separating trees and simple congruences of the weak order
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913092378558464 |
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| author | Barnard, Emily Novelli, Jean-Christophe Pilaud, Vincent |
| author_facet | Barnard, Emily Novelli, Jean-Christophe Pilaud, Vincent |
| contents | A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a combinatorial description of the vertices of the corresponding quotientopes in terms of separating trees. This also yields a combinatorial description of all faces of the corresponding quotientopes. We finally explore algebraic aspects of separating trees, in particular their connections with quiver representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separating trees and simple congruences of the weak order Barnard, Emily Novelli, Jean-Christophe Pilaud, Vincent Combinatorics 06B10, 52B11, 52B12 A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a combinatorial description of the vertices of the corresponding quotientopes in terms of separating trees. This also yields a combinatorial description of all faces of the corresponding quotientopes. We finally explore algebraic aspects of separating trees, in particular their connections with quiver representation theory. |
| title | Separating trees and simple congruences of the weak order |
| topic | Combinatorics 06B10, 52B11, 52B12 |
| url | https://arxiv.org/abs/2503.15053 |