title: Knots cascade detected by a monotonically decreasing sequence of values.
abstract: Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.
authors.affiliation: Beijing-Dublin International College &Institute of Theoretical Physics, Beijing University of Technology, 100 Pingleyuan, Beijing 100124, P.R. China.
authors.forename: Xin
authors.initials: X
authors.lastname: Liu
authors.affiliation: Department of Mathematics &Applications, University of Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy.
authors.forename: Renzo L
authors.initials: RL
authors.lastname: Ricca
mesh_terms: D000465:Algorithms; D001483:Base Sequence; D004247:DNA / Q000737:chemistry* / Q000235:genetics; D007700:Kinetics; D008958:Models, Molecular; D009690:Nucleic Acid Conformation; D010957:Plasmids / Q000737:chemistry / Q000235:genetics; D013997:Time Factors
chemical_list: D004247:DNA