On the strength of chromatic symmetric homology for graphs

Alex Chandler, Radmila Sazdanovic, Salvatore Stella, Martha Yip

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Article number102559
JournalAdvances in Applied Mathematics
StatePublished - Sep 2023

Bibliographical note

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© 2023 Elsevier Inc.


  • Categorification
  • Chromatic symmetric function

ASJC Scopus subject areas

  • Applied Mathematics


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