A Dynkin diagram classification theorem arising from a combinatorial problem
A poset P is vertex-labelable if there exists a rational-valued function \(\pi\) on P such that, for every order ideal \(I\subseteq P\), we have \[ \sum_{x\quad \max imal\quad in\quad I}\pi (x)-| I| =\sum_{y\quad \min imal\quad in\quad P-I}\pi (y)-| P-I|. \] The poset of all order ideals in a vertex-labelable poset is rank symmetric, rank unimodal and strongly Sperner. The author presents a complete classification of vertex-labelable posets.
scientific article; zbMATH DE number 4041977
scientific article