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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04489 |
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| _version_ | 1866915664332062720 |
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| author | Castillo, Federico de la Fuente, Damian Libedinsky, Nicolas Plaza, David |
| author_facet | Castillo, Federico de la Fuente, Damian Libedinsky, Nicolas Plaza, David |
| contents | We derive a formula for computing the size of lower Bruhat intervals for elements in the dominant cone of an affine Weyl group of type $A$. This enumeration problem is reduced to counting lattice points in certain polyhedra. Our main tool is a decomposition -- or tiling -- of each interval into smaller, combinatorially tractable pieces, which we call paper boats. We also conjecture a generalization of this formula to all affine Weyl groups, restricted to elements in the lowest two-sided Kazhdan-Lusztig cell, which contains almost all of the elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paper BOAT Castillo, Federico de la Fuente, Damian Libedinsky, Nicolas Plaza, David Combinatorics Group Theory Representation Theory We derive a formula for computing the size of lower Bruhat intervals for elements in the dominant cone of an affine Weyl group of type $A$. This enumeration problem is reduced to counting lattice points in certain polyhedra. Our main tool is a decomposition -- or tiling -- of each interval into smaller, combinatorially tractable pieces, which we call paper boats. We also conjecture a generalization of this formula to all affine Weyl groups, restricted to elements in the lowest two-sided Kazhdan-Lusztig cell, which contains almost all of the elements. |
| title | Paper BOAT |
| topic | Combinatorics Group Theory Representation Theory |
| url | https://arxiv.org/abs/2504.04489 |