Schur log-concavity and the quantum Pascal triangle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909809771544576 |
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| author | Gutiérrez, Álvaro Krattenthaler, Christian |
| author_facet | Gutiérrez, Álvaro Krattenthaler, Christian |
| contents | We say a sequence $f_0, f_1, f_2, \ldots$ of symmetric functions is Schur log-concave if $f_n^2 - f_{n-1}f_{n+1}$ is Schur positive for all $n\ge1$. We conjecture that a very general class of sequences of Schur functions satisfies this property, and show it for sequences of Schur functions indexed by partitions with growing first part and column. Our findings are related to work of Lam, Postnikov and Pylyavskyy on Schur positivity, and of Butler, Sagan, and the second author on $q$-log-concavity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schur log-concavity and the quantum Pascal triangle Gutiérrez, Álvaro Krattenthaler, Christian Combinatorics Primary 05E05, Secondary 05A30 We say a sequence $f_0, f_1, f_2, \ldots$ of symmetric functions is Schur log-concave if $f_n^2 - f_{n-1}f_{n+1}$ is Schur positive for all $n\ge1$. We conjecture that a very general class of sequences of Schur functions satisfies this property, and show it for sequences of Schur functions indexed by partitions with growing first part and column. Our findings are related to work of Lam, Postnikov and Pylyavskyy on Schur positivity, and of Butler, Sagan, and the second author on $q$-log-concavity. |
| title | Schur log-concavity and the quantum Pascal triangle |
| topic | Combinatorics Primary 05E05, Secondary 05A30 |
| url | https://arxiv.org/abs/2509.22648 |