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June 3, 20260 citationsOpen Access

Polynomial Invariants of Virtual Doodles and Flat Virtual Knots

JKJoonoh KimKKKyoung-Tark Kim

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. (2026) studied this question.

synapsesocial.com/papers/6a1fc550dee9eb8c0dce6b43https://doi.org/10.18910/104862
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