Shuffle theorems and sandpiles
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911758135853056 |
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| author | D'Adderio, Michele Dukes, Mark Iraci, Alessandro Lazar, Alexander Borgne, Yvan Le Wyngaerd, Anna Vanden |
| author_facet | D'Adderio, Michele Dukes, Mark Iraci, Alessandro Lazar, Alexander Borgne, Yvan Le Wyngaerd, Anna Vanden |
| contents | We provide an explicit description of the recurrent configurations of the sandpile model on a family of graphs $\widehat{G}_{μ,ν}$, which we call clique-independent graphs, indexed by two compositions $μ$ and $ν$. Moreover, we define a delay statistic on these configurations, and we show that, together with the usual level statistic, it can be used to provide a new combinatorial interpretation of the celebrated shuffle theorem of Carlsson and Mellit. More precisely, we will see how to interpret the polynomials $\langle \nabla e_n, e_μh_ν\rangle$ in terms of these configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shuffle theorems and sandpiles D'Adderio, Michele Dukes, Mark Iraci, Alessandro Lazar, Alexander Borgne, Yvan Le Wyngaerd, Anna Vanden Combinatorics Mathematical Physics 05E05, 82B20 We provide an explicit description of the recurrent configurations of the sandpile model on a family of graphs $\widehat{G}_{μ,ν}$, which we call clique-independent graphs, indexed by two compositions $μ$ and $ν$. Moreover, we define a delay statistic on these configurations, and we show that, together with the usual level statistic, it can be used to provide a new combinatorial interpretation of the celebrated shuffle theorem of Carlsson and Mellit. More precisely, we will see how to interpret the polynomials $\langle \nabla e_n, e_μh_ν\rangle$ in terms of these configurations. |
| title | Shuffle theorems and sandpiles |
| topic | Combinatorics Mathematical Physics 05E05, 82B20 |
| url | https://arxiv.org/abs/2401.06488 |