Coloring-allowed Invariants and the 4-phases Functions of Knotoids

Haocong Chen; Jiacheng An; Fengling Li

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arXiv · 2606.10362

Coloring-allowed Invariants and the 4-phases Functions of Knotoids

Haocong Chen·Jiacheng An·Fengling Li

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Abstract

In recent years, numerous polynomial invariants of knotoids have been constructed, some of which are defined with the signs of the crossings. In this paper, the coloring-allowed invariants of planar knotoids, which is a class of planar knotoid invariants defined with the coloring number are introduced. We demonstrate several basic properties of the coloring number and some examples of coloring-allowed invariants, among which the 4-phases functions are discussed in detail, including their invariance and properties.

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BibTeX RIS

Haocong Chen, Jiacheng An, Fengling Li. 2026-06-09. Coloring-allowed Invariants and the 4-phases Functions of Knotoids. https://arxiv.org/abs/2606.10362

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