{"paper":{"title":"The Redei--Berge symmetric function of a directed graph","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darij Grinberg, Richard P. Stanley","submitted_at":"2023-07-10T04:58:21Z","abstract_excerpt":"Let $D=\\left( V,A\\right) $ be a digraph with $n$ vertices, where each arc $a\\in A$ is a pair $\\left( u,v\\right) $ of two vertices. We study the \\emph{Redei--Berge symmetric function} $U_{D}$, defined as the quasisymmetric function% \\[ \\sum L_{\\operatorname*{Des}\\left( w,D\\right) ,\\ n}\\in\\operatorname*{QSym}. \\] Here, the sum ranges over all lists $w=\\left( w_{1},w_{2},\\ldots ,w_{n}\\right) $ that contain each vertex of $D$ exactly once, and the corresponding addend is% \\[ L_{\\operatorname*{Des}\\left( w,D\\right) ,\\ n}:=\\sum_{\\substack{i_{1}\\leq i_{2}\\leq\\cdots\\leq i_{n};\\\\i_{p}