Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909630352850944 |
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| author | Nguyen, Chau Nguyen, Son Woodruff, Dora |
| author_facet | Nguyen, Chau Nguyen, Son Woodruff, Dora |
| contents | We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized Littlewood--Richardson coefficients for Temperley--Lieb immanants of Jacobi--Trudi matrices. We will also show that our rule behaves well with Bender--Knuth involutions, recovering the symmetry of Littlewood--Richardson coefficients. As an application, we use our rule to prove a special case of a Schur log-concavity conjecture by Lam--Postnikov--Pylyavskyy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity Nguyen, Chau Nguyen, Son Woodruff, Dora Combinatorics We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized Littlewood--Richardson coefficients for Temperley--Lieb immanants of Jacobi--Trudi matrices. We will also show that our rule behaves well with Bender--Knuth involutions, recovering the symmetry of Littlewood--Richardson coefficients. As an application, we use our rule to prove a special case of a Schur log-concavity conjecture by Lam--Postnikov--Pylyavskyy. |
| title | Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.00349 |