Commun. Korean Math. Soc. 2024; 39(1): 223-245
Online first article January 28, 2024 Printed January 31, 2024
https://doi.org/10.4134/CKMS.c220360
Copyright © The Korean Mathematical Society.
Jose Ceniceros, Mohamed Elhamdadi, Josef Komissar, Hitakshi Lahrani
Hamilton College; University of South Florida; Syracuse University; University of South Florida
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.
Keywords: Stuck knots, quandles, stuquandles, arc diagrams, RNA foldings
MSC numbers: Primary 57K10, 57M25, 57Z05
Supported by: The second author was partially supported by Simons Foundation collaboration grant 712462.
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