Some conjectures on the Schur expansion of Jack polynomials
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866915800095391744 |
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| author | Alexandersson, Per Haglund, James Wang, George |
| author_facet | Alexandersson, Per Haglund, James Wang, George |
| contents | We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_12763 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Some conjectures on the Schur expansion of Jack polynomials Alexandersson, Per Haglund, James Wang, George Combinatorics Primary 05E05, Secondary 05A15 We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases. |
| title | Some conjectures on the Schur expansion of Jack polynomials |
| topic | Combinatorics Primary 05E05, Secondary 05A15 |
| url | https://arxiv.org/abs/1810.12763 |