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PreprintarXiv licencearXiv

The chromatic noncommutative symmetric function of oriented trees

  • Lingxiao Hao
  • Shenglin Zhu
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Abstract

A long-standing question is whether chromatic symmetric functions can distinguish non-isomorphic trees. Campbell introduced chromatic noncommutative symmetric functions for digraphs, which lift chromatic symmetric functions to NSym, and asked to what extent they can distinguish non-isomorphic oriented trees. In this article, we prove that chromatic noncommutative symmetric functions can reconstruct oriented stars, oriented double stars, some oriented caterpillars, and some oriented paths.

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Cite

BibTeXRIS
BibTeX
@misc{hao2026chromatic,
  title = {{The chromatic noncommutative symmetric function of oriented trees}},
  author = {Lingxiao Hao and Shenglin Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.03436},
  eprint = {2606.03436},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.03436},
}
RIS
TY  - UNPB
TI  - The chromatic noncommutative symmetric function of oriented trees
AU  - Lingxiao Hao
AU  - Shenglin Zhu
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.03436
UR  - https://arxiv.org/abs/2606.03436
AB  - A long-standing question is whether chromatic symmetric functions can distinguish non-isomorphic trees. Campbell introduced chromatic noncommutative symmetric functions for digraphs, which lift chromatic symmetric functions to NSym, and asked to what extent they can distinguish non-isomorphic oriented trees. In this article, we prove that chromatic noncommutative symmetric functions can reconstruct oriented stars, oriented double stars, some oriented caterpillars, and some oriented paths.
ER  -