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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.16168 |
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| _version_ | 1866913685487747072 |
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| author | Le, Tuong Ouyang, Shuge Tao, Leo Restivo, Joseph Zhang, Angelina |
| author_facet | Le, Tuong Ouyang, Shuge Tao, Leo Restivo, Joseph Zhang, Angelina |
| contents | Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pipe dreams. Quantum double Schubert polynomials are polynomial representatives of Schubert classes in the torus-equivariant quantum cohomology of the complete flag variety, but no analogous combinatorial formulation had been discovered. We introduce a generalization of the bumpless pipe dreams called quantum bumpless pipe dreams, giving a novel combinatorial formula for quantum double Schubert polynomials as a sum of binomial weights of quantum bumpless pipe dreams. We give a bijective proof for this formula by showing that the sum of binomial weights satisfies a defining transition equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum bumpless pipe dreams Le, Tuong Ouyang, Shuge Tao, Leo Restivo, Joseph Zhang, Angelina Combinatorics 05E05 Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pipe dreams. Quantum double Schubert polynomials are polynomial representatives of Schubert classes in the torus-equivariant quantum cohomology of the complete flag variety, but no analogous combinatorial formulation had been discovered. We introduce a generalization of the bumpless pipe dreams called quantum bumpless pipe dreams, giving a novel combinatorial formula for quantum double Schubert polynomials as a sum of binomial weights of quantum bumpless pipe dreams. We give a bijective proof for this formula by showing that the sum of binomial weights satisfies a defining transition equation. |
| title | Quantum bumpless pipe dreams |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2403.16168 |