Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Jingxuan, Liu, Feihu, Xin, Guoce
Institution: Capital Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6054591771
OpenAlex ID: W4405094885