The nonsymmetric compositional Delta theorem
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911585283342336 |
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| author | Qiu, Dun Zhang, Minhao |
| author_facet | Qiu, Dun Zhang, Minhao |
| contents | Extending the symmetric framework of D'Adderio and Mellit, we establish a nonsymmetric generalization of the compositional Delta theorem. Building on Blasiak et al.'s theory of flagged LLT polynomials, we derive signed and unsigned nonsymmetric identities evaluated in terms of flagged LLT polynomials. Furthermore, by introducing nonsymmetric variants of the $\nabla$ and $τ^*$ operators, we obtain a novel operator formulation. We show that applying Weyl symmetrization to these nonsymmetric identities systematically recovers the original compositional Delta theorem. Finally, we propose analogous conjectures regarding stable atom positivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10226 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The nonsymmetric compositional Delta theorem Qiu, Dun Zhang, Minhao Combinatorics 05E05 (Primary) 05E10, 33D52, 16T30 (Secondary) Extending the symmetric framework of D'Adderio and Mellit, we establish a nonsymmetric generalization of the compositional Delta theorem. Building on Blasiak et al.'s theory of flagged LLT polynomials, we derive signed and unsigned nonsymmetric identities evaluated in terms of flagged LLT polynomials. Furthermore, by introducing nonsymmetric variants of the $\nabla$ and $τ^*$ operators, we obtain a novel operator formulation. We show that applying Weyl symmetrization to these nonsymmetric identities systematically recovers the original compositional Delta theorem. Finally, we propose analogous conjectures regarding stable atom positivity. |
| title | The nonsymmetric compositional Delta theorem |
| topic | Combinatorics 05E05 (Primary) 05E10, 33D52, 16T30 (Secondary) |
| url | https://arxiv.org/abs/2604.10226 |