On the strength of chromatic symmetric homology for graphs

In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric functio...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 150; p. 102559
Main Authors Chandler, Alex, Sazdanovic, Radmila, Stella, Salvatore, Yip, Martha
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2023
Subjects
Categorification
Chromatic symmetric function
05C10
05E10
Chromatic symmetric function
Categorification
05C15
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Summary:In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric function. We exhibit three pairs of graphs where each pair has the same chromatic symmetric function but distinct homology over C as Sn-modules. We also show that integral chromatic symmetric homology contains torsion, and based on computations, conjecture that Z2-torsion in bigrading (1,0) detects nonplanarity in the graph.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2023.102559