The Redei--Berge symmetric function of a directed graph

2023/07/10 by Grinberg, Darij, Stanley, Richard P. · 3 citations
#05A05 #05A19 #05C30 #05E05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.05569

Abstract

Let D=( V,A) be a digraph with n vertices, where each arc a∈ A is a pair ( u,v) of two vertices. We study the Redei--Berge symmetric function U_D, defined as the quasisymmetric function% ∑ L_\operatorname*Des( w,D) , n∈\operatorname*QSym. Here, the sum ranges over all lists w=( w₁,w₂,… ,w_n) that contain each vertex of D exactly once, and the corresponding addend is% \[ L_\operatorname*Des( w,D) , n:=∑_\substacki₁≤ i₂≤⋯≤ i_n;\ı_p

Cited by

• The connection between the chromatic function and the Redei-Berge function
• Linear function of a poset
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Related

• The Redei-Berge Hopf algebra of digraphs
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• Linear function of a poset