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arXiv · 2606.03436

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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Lingxiao Hao, Shenglin Zhu. 2026-09-08. The chromatic noncommutative symmetric function of oriented trees. https://arxiv.org/abs/2606.03436

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