Smirnov words and the Delta Conjectures
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910294492577792 |
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| author | Iraci, Alessandro Nadeau, Philippe Wyngaerd, Anna Vanden |
| author_facet | Iraci, Alessandro Nadeau, Philippe Wyngaerd, Anna Vanden |
| contents | We provide a combinatorial interpretation of the symmetric function $\left.Θ_{e_k}Θ_{e_l}\nabla e_{n-k-l}\right|_{t=0}$ in terms of segmented Smirnov words. The motivation for this work is the study of a diagonal coinvariant ring with one set of commuting and two sets of anti-commuting variables, whose Frobenius characteristic is conjectured to be the symmetric function in question. Furthermore, this function is related to the Delta conjectures. Our work is a step towards a unified formulation of the two versions, as we prove a unified Delta theorem at $t=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03956 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smirnov words and the Delta Conjectures Iraci, Alessandro Nadeau, Philippe Wyngaerd, Anna Vanden Combinatorics 05E05, 05E10 We provide a combinatorial interpretation of the symmetric function $\left.Θ_{e_k}Θ_{e_l}\nabla e_{n-k-l}\right|_{t=0}$ in terms of segmented Smirnov words. The motivation for this work is the study of a diagonal coinvariant ring with one set of commuting and two sets of anti-commuting variables, whose Frobenius characteristic is conjectured to be the symmetric function in question. Furthermore, this function is related to the Delta conjectures. Our work is a step towards a unified formulation of the two versions, as we prove a unified Delta theorem at $t=0$. |
| title | Smirnov words and the Delta Conjectures |
| topic | Combinatorics 05E05, 05E10 |
| url | https://arxiv.org/abs/2312.03956 |