On $P$-partitions Extended by Two-Rowed Plane Partitions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929616831119360 |
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| author | Li, Jingxuan Liu, Feihu Xin, Guoce |
| author_facet | Li, Jingxuan Liu, Feihu Xin, Guoce |
| contents | Inspired by Gansner's elegant $k$-trace generating function for rectangular plane partitions, we introduce two novel operators, $φ_{z}$ and $ψ_{z}$, along with their combinatorial interpretations. Through these operators, we derive a new formula for $P$-partitions of posets extended by two-rowed plane partitions. This formula allows us to compute explicit enumerative generating functions for various classes of $P$-partitions. Our findings encompass skew plane partitions, diamond-related two-rowed plane partitions, an extended $V$-poset, and ladder poset extensions, enriching the theory of $P$-partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $P$-partitions Extended by Two-Rowed Plane Partitions Li, Jingxuan Liu, Feihu Xin, Guoce Combinatorics Primary 05A15, Secondary 05A17, 11P81 Inspired by Gansner's elegant $k$-trace generating function for rectangular plane partitions, we introduce two novel operators, $φ_{z}$ and $ψ_{z}$, along with their combinatorial interpretations. Through these operators, we derive a new formula for $P$-partitions of posets extended by two-rowed plane partitions. This formula allows us to compute explicit enumerative generating functions for various classes of $P$-partitions. Our findings encompass skew plane partitions, diamond-related two-rowed plane partitions, an extended $V$-poset, and ladder poset extensions, enriching the theory of $P$-partitions. |
| title | On $P$-partitions Extended by Two-Rowed Plane Partitions |
| topic | Combinatorics Primary 05A15, Secondary 05A17, 11P81 |
| url | https://arxiv.org/abs/2412.03971 |