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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.14975 |
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| _version_ | 1866912573467656192 |
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| author | Pan, Jianping Pappe, Joseph Poh, Wencin Schilling, Anne |
| author_facet | Pan, Jianping Pappe, Joseph Poh, Wencin Schilling, Anne |
| contents | Whereas set-valued tableaux are the combinatorial objects associated to stable Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. In this paper, we define a novel uncrowding algorithm for hook-valued tableaux. The algorithm "uncrowds" the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. We prove that our uncrowding algorithm intertwines with crystal operators. An alternative uncrowding algorithm that "uncrowds" the entries in the leg instead of the arm of the hooks is also given. As an application of uncrowding, we obtain various expansions of the canonical Grothendieck polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_14975 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uncrowding algorithm for hook-valued tableaux Pan, Jianping Pappe, Joseph Poh, Wencin Schilling, Anne Combinatorics Primary 05E05, 05E10, Secondary 14N10, 14N15, 20G42 Whereas set-valued tableaux are the combinatorial objects associated to stable Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. In this paper, we define a novel uncrowding algorithm for hook-valued tableaux. The algorithm "uncrowds" the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. We prove that our uncrowding algorithm intertwines with crystal operators. An alternative uncrowding algorithm that "uncrowds" the entries in the leg instead of the arm of the hooks is also given. As an application of uncrowding, we obtain various expansions of the canonical Grothendieck polynomials. |
| title | Uncrowding algorithm for hook-valued tableaux |
| topic | Combinatorics Primary 05E05, 05E10, Secondary 14N10, 14N15, 20G42 |
| url | https://arxiv.org/abs/2012.14975 |