대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권1호
  • /
  • Pages.223-245
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  • 2024
  • /
  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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RNA FOLDINGS AND STUCK KNOTS

  • 투고 : 2022.12.13
  • 심사 : 2023.09.18
  • 발행 : 2024.01.31
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초록

We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots emphasize a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.

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과제정보

The authors would like to thank the referee for the fruitful comments which improved the paper. The authors would also like to thank Willi Kepplinger for his comments on an earlier version of this article.

참고문헌

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