On P-partitions Extended by Two-Rowed Plane Partitions

2024/12/05 by Jingxuan Li, Feihu Liu, Li, Jingxuan +3 · 1 citation
Mathematics · Computer Science · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Digital Image Processing Techniques

paper · pdf · doi:10.48550/arxiv.2412.03971

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.

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