RSK correspondence for King tableaux with Berele insertion
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914354661687296 |
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| author | Kobayashi, Masato Matsumura, Tomoo |
| author_facet | Kobayashi, Masato Matsumura, Tomoo |
| contents | We establish a bijective RSK correspondence of type C for King tableaux with Berele insertion as a reformulation of Sundaram's correspondence (1986). For its $Q$-symbol, we make use of semistandard oscillating tableaux (SSOT), a new object which Lee (2025) introduced. Further, we show hidden duality of Cauchy identity through RSK correspondences of type A and C. Finally, we prove that the generating function of SSOT is symmetric by constructing a new sort of Bender-Knuth involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | RSK correspondence for King tableaux with Berele insertion Kobayashi, Masato Matsumura, Tomoo Combinatorics 2020 Primary:05E05, Secondary:05E10, 05E18 We establish a bijective RSK correspondence of type C for King tableaux with Berele insertion as a reformulation of Sundaram's correspondence (1986). For its $Q$-symbol, we make use of semistandard oscillating tableaux (SSOT), a new object which Lee (2025) introduced. Further, we show hidden duality of Cauchy identity through RSK correspondences of type A and C. Finally, we prove that the generating function of SSOT is symmetric by constructing a new sort of Bender-Knuth involution. |
| title | RSK correspondence for King tableaux with Berele insertion |
| topic | Combinatorics 2020 Primary:05E05, Secondary:05E10, 05E18 |
| url | https://arxiv.org/abs/2506.06951 |