$[k]\times P_{n,s}$ 上两个反链多项式的公共交织器
A common interleaver for two antichain polynomials on $[k]$$\times$ $P_{n,s}$
- College of Science, Jiujiang University（九江学院理学院）
- School of Mathematics, Foshan University（佛山大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过将Jiang的方法推广到两行Ferrers形状，证明了关于反链生成多项式的猜想4.2，并利用实稳定性和Chudnovsky-Seymour准则构造公共交织器。
AI中文摘要：
第一作者与Dong \cite{DD} 提出了关于反链生成多项式的三个猜想。Jiang \cite{Jiang} 最近证明了猜想4.3和4.5，涉及实根性和\\(\gamma\\)-正性。我们通过将其方法从 \\([k]\times [2] \times [n]\\) 调整到 \\([k]\times P_{n,s} \\) 来证明猜想4.2，其中 \\(P_{n,s}\\) 是一个两行Ferrers形状。我们建立了与相邻形状相关的双变量多项式族的实稳定性，然后应用Chudnovsky-Seymour相容性准则获得一个公共交织器。如 \cite{DD} 所述，猜想4.2也蕴含猜想4.3。
英文摘要：
The first author and Dong \cite{DD} proposed three conjectures on antichain generating polynomials. Jiang \cite{Jiang} recently proved Conjectures 4.3 and 4.5, concerning real-rootedness and \(γ\)-positivity. We prove Conjecture 4.2 by adapting his method from \([k]\times [2] \times [n]\) to \([k]\times P_{n,s} \), where \(P_{n,s}\) is a two-row Ferrers shape. We establish real stability for a family of bivariate polynomials associated with adjacent shapes, then apply the Chudnovsky-Seymour compatibility criterion to obtain a common interleaver. As noted in \cite{DD}, Conjecture 4.2 also implies Conjecture 4.3.
