2024/07/26 by Stefan Mitrovic, Mitrovic, Stefan, Tanja Stojadinovic +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2407.18608
openalex publication_date 2024/07/26 · openalex created_date 2024/09/30 · openalex updated_date 2026/07/28
Stanley and Grinberg introduced the symmetric function associated to digraphs, called the Redei-Berge symmetric function. In [8] is shown that this symmetric function arises from a suitable structure of combinatorial Hopf algebra on digraphs. In this paper, we introduce two new combinatorial Hopf algebras of posets and permutations and define corresponding Redei-Berge functions for them. By using both theories, of symmetric functions and of combinatorial Hopf algebras, we prove many properties of the Redei-Berge function. These include some forms of deletion-contraction property, which make it similar to the chromatic symmetric function. We also find some invariants of digraphs that are detected by the Redei-Berge function.