A combinatorial skewing formula for the Rise Delta Theorem
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916366397734912 |
|---|---|
| author | Gillespie, Maria Gorsky, Eugene Griffin, Sean T. |
| author_facet | Gillespie, Maria Gorsky, Eugene Griffin, Sean T. |
| contents | We prove that the symmetric function $Δ'_{e_{k-1}}e_n$ appearing in the Delta Conjecture can be obtained from the symmetric function in the Rational Shuffle Theorem by applying a Schur skewing operator. This generalizes a formula by the first and third authors for the Delta Conjecture at $t=0$, and follows from work of Blasiak, Haiman, Morse, Pun, and Seelinger.
Our main result is that we also provide a purely combinatorial proof of this skewing identity, giving a new proof of the Rise Delta Theorem from the Rational Shuffle Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A combinatorial skewing formula for the Rise Delta Theorem Gillespie, Maria Gorsky, Eugene Griffin, Sean T. Combinatorics 05E05 We prove that the symmetric function $Δ'_{e_{k-1}}e_n$ appearing in the Delta Conjecture can be obtained from the symmetric function in the Rational Shuffle Theorem by applying a Schur skewing operator. This generalizes a formula by the first and third authors for the Delta Conjecture at $t=0$, and follows from work of Blasiak, Haiman, Morse, Pun, and Seelinger. Our main result is that we also provide a purely combinatorial proof of this skewing identity, giving a new proof of the Rise Delta Theorem from the Rational Shuffle Theorem. |
| title | A combinatorial skewing formula for the Rise Delta Theorem |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2408.12543 |