可数n自由序集的交替托马斯猜想的证明

Order Pub Date : 2023-11-20 DOI:10.1007/s11083-023-09650-w

Davoud Abdi

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摘要

无n偏序集是指其可比性图不嵌入具有四个顶点的诱导路径的偏序集。利用可数无n序集和一些标记有序树的拟良序性质，证明了一个可数无n序集有一个或无穷多个兄弟，直至同构。这部分地证明了托马斯为这门课提出的一个猜想。

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A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets

An N-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable N-free posets and some labelled ordered trees to show that a countable N-free poset has one or infinitely many siblings, up to isomorphism. This, partially proves a conjecture stated by Thomassé for this class.

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