2014/04/29 by Ryan Kaliszewski, Kaliszewski, Ryan · 2 citations
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.1404.7531
openalex publication_date 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The chromatic symmetric function of a graph is a generalization of the chromatic polynomial. The key motivation for studying the structure of a chromatic symmetric function is to answer positivity conjectures by Stanley in 1995 and Gasharov in 1996. As a symmetric function one can write the chromatic symmetric function in the basis of Schur functions. In this paper we address the positivity of the Schur coefficients when the parameter of the Schur function is a hook shape. Furthermore, when a graph is the incomparability graph of a poset with specific properties we construct a correspondence between acyclic orientations of the graph and P-tableaux with a hook shape.