On a Pieri-like rule for the Petrie symmetric functions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908676801953792 |
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| author | Jin, Emma Yu Jing, Naihuan Liu, Ning |
| author_facet | Jin, Emma Yu Jing, Naihuan Liu, Ning |
| contents | A $k$-ribbon tiling is a decomposition of a connected skew diagram into disjoint ribbons of size $k$. In this paper, we establish a connection between a subset of $k$-ribbon tilings and Petrie symmetric functions, thus providing a combinatorial interpretation for the coefficients in a Pieri-like rule for the Petrie symmetric functions due to Grinberg (Algebr. Comb. 5 (2022), no. 5, 947-1013). This also extends a result by Cheng, Chou and Eu et al. (Proc. Amer. Math. Soc. 151 (2023), no. 5, 1839-1854). As a bonus, our findings can be effectively utilized to derive certain specializations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Pieri-like rule for the Petrie symmetric functions Jin, Emma Yu Jing, Naihuan Liu, Ning Combinatorics 05E05, 05A17 A $k$-ribbon tiling is a decomposition of a connected skew diagram into disjoint ribbons of size $k$. In this paper, we establish a connection between a subset of $k$-ribbon tilings and Petrie symmetric functions, thus providing a combinatorial interpretation for the coefficients in a Pieri-like rule for the Petrie symmetric functions due to Grinberg (Algebr. Comb. 5 (2022), no. 5, 947-1013). This also extends a result by Cheng, Chou and Eu et al. (Proc. Amer. Math. Soc. 151 (2023), no. 5, 1839-1854). As a bonus, our findings can be effectively utilized to derive certain specializations. |
| title | On a Pieri-like rule for the Petrie symmetric functions |
| topic | Combinatorics 05E05, 05A17 |
| url | https://arxiv.org/abs/2406.00581 |