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Polynomial Invariants of Virtual Doodles and Flat Virtual Knots | Synapse

June 3, 2026Open Access

Polynomial Invariants of Virtual Doodles and Flat Virtual Knots

Key Points

To introduce polynomial invariants of virtual doodles using a state model and integer labeling.
Combined a state model with integer labeling to analyze flat virtual knot diagrams.
Introduced new invariants to examine differences in doodle diagrams.
Showed that doodle diagram d₄.₁ is different from doodle diagram d₄.₄ using the new invariants.

Abstract

In this paper, we introduce new polynomial invariants of virtual doodles obtained by combining a state model with an integer labeling to flat virtual knot diagrams. Using our invariants we show that the doodle diagram d₄.₁ is different from the doodle diagram d₄.₄.

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Cite This Study

Kim et al. (Wed,) studied this question.

synapsesocial.com/papers/6a1fc550dee9eb8c0dce6b43 https://doi.org/https://doi.org/10.18910/104862

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