Gamma vectors of partitioned permutohedra
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915266070315008 |
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| author | Horiguchi, Tatsuya Masuda, Mikiya Sato, Takashi Shareshian, John Song, Jongbaek |
| author_facet | Horiguchi, Tatsuya Masuda, Mikiya Sato, Takashi Shareshian, John Song, Jongbaek |
| contents | We determine that $γ$-vectors of partitioned permutohedra, thereby generalizing a result of Foata and Schützenberger. Our result is closely related to a result of Athanasiadis on the representation of the symmetric group on the cohomology of the permutohedral variety. We explain how to derive Athanasiadis' result from ours and vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gamma vectors of partitioned permutohedra Horiguchi, Tatsuya Masuda, Mikiya Sato, Takashi Shareshian, John Song, Jongbaek Combinatorics Algebraic Geometry Representation Theory 05E10, 14M25, 20C30, 52B05 We determine that $γ$-vectors of partitioned permutohedra, thereby generalizing a result of Foata and Schützenberger. Our result is closely related to a result of Athanasiadis on the representation of the symmetric group on the cohomology of the permutohedral variety. We explain how to derive Athanasiadis' result from ours and vice versa. |
| title | Gamma vectors of partitioned permutohedra |
| topic | Combinatorics Algebraic Geometry Representation Theory 05E10, 14M25, 20C30, 52B05 |
| url | https://arxiv.org/abs/2405.09242 |