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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2110.05648 |
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| _version_ | 1866908932028497920 |
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| author | Aliniaeifard, Farid Li, Shu Xiao |
| author_facet | Aliniaeifard, Farid Li, Shu Xiao |
| contents | The descent-to-peak map serves as a bridge between algebra and combinatorics. We use it as a tool for proving the equidistribution of peak and valley sets of standard Young tableaux with a very short argument. We also introduce a new shuffle basis of quasisymmetric functions whose elements are eigenvectors of the descent-to-peak map. Using this basis, we then extend the notion of the peak algebra and of the descent-to-peak map to shuffle, tensor, and symmetric algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_05648 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extending the descent-to-peak map and its applications Aliniaeifard, Farid Li, Shu Xiao Combinatorics The descent-to-peak map serves as a bridge between algebra and combinatorics. We use it as a tool for proving the equidistribution of peak and valley sets of standard Young tableaux with a very short argument. We also introduce a new shuffle basis of quasisymmetric functions whose elements are eigenvectors of the descent-to-peak map. Using this basis, we then extend the notion of the peak algebra and of the descent-to-peak map to shuffle, tensor, and symmetric algebras. |
| title | Extending the descent-to-peak map and its applications |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2110.05648 |