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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/2406.01510 |
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| _version_ | 1866911414654861312 |
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| author | Nadeau, Philippe Spink, Hunter Tewari, Vasu |
| author_facet | Nadeau, Philippe Spink, Hunter Tewari, Vasu |
| contents | We develop a quasisymmetric analogue of the combinatorial theory of Schubert polynomials and the associated divided difference operators. Our counterparts are "forest polynomials", and a new family of linear operators, whose theory of compositions is governed by forests and the "Thompson monoid". Our approach extends naturally to $m$-colored quasisymmetric functions.
We then give several applications of our theory to fundamental quasisymmetric functions, the study of quasisymmetric coinvariant rings and their associated harmonics, and positivity results for various expansions. In particular we resolve a conjecture of Aval-Bergeron-Li regarding quasisymmetric harmonics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasisymmetric divided differences Nadeau, Philippe Spink, Hunter Tewari, Vasu Combinatorics We develop a quasisymmetric analogue of the combinatorial theory of Schubert polynomials and the associated divided difference operators. Our counterparts are "forest polynomials", and a new family of linear operators, whose theory of compositions is governed by forests and the "Thompson monoid". Our approach extends naturally to $m$-colored quasisymmetric functions. We then give several applications of our theory to fundamental quasisymmetric functions, the study of quasisymmetric coinvariant rings and their associated harmonics, and positivity results for various expansions. In particular we resolve a conjecture of Aval-Bergeron-Li regarding quasisymmetric harmonics. |
| title | Quasisymmetric divided differences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.01510 |