Entanglement complexity of graphs in Z3

DOI10.1017/S0305004100075174zbMath0769.57007OpenAlexW2034647396MaRDI QIDQ3994049

De Witt Sumners, Christine E. Soteros, Stuart G. Whittington

Publication date: 13 August 1992

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100075174

zbMATH Keywords

knotscrossing numbergenusbraid indexbridge numberunknotting numbermeasures of complexityminor indexcomplexity of graphs in 3-spaceLaurent knot polynomial

Mathematics Subject Classification ID

Related Items (29)

The distribution of knots in the Petaluma model ⋮ The Curvature of Lattice Knots ⋮ Knotting statistics for polygons in lattice tubes ⋮ UPPER BOUNDS ON LINKING NUMBERS OF THICK LINKS ⋮ Models of random knots ⋮ Random state transitions of knots: a first step towards modeling unknotting by type II topoisomerases ⋮ Random colorings in manifolds ⋮ Automatic calculation of minimum crossing numbers of 3-braids. ⋮ The lace expansion on a tree with application to networks of self-avoiding walks ⋮ Statics and dynamics of DNA knotting ⋮ A random walk with Stu Whittington ⋮ New evidence on the asymptotics of knotted lattice polygons via local strand-passage models ⋮ KNOTTED 2-SPHERES IN TUBES IN Z⁴ ⋮ KNOTS, SLIPKNOTS, AND EPHEMERAL KNOTS IN RANDOM WALKS AND EQUILATERAL POLYGONS ⋮ Polymers with spatial or topological constraints: theoretical and computational results ⋮ ON TOPOLOGICAL CORRELATIONS IN TRIVIAL KNOTS: FROM BROWNIAN BRIDGES TO CRUMPLED GLOBULES ⋮ THE LINKING PROBABILITY FOR 2-COMPONENT LINKS WHICH SPAN A LATTICE TUBE ⋮ Random knots in 3-dimensional 3-colour percolation: numerical results and conjectures ⋮ Statistical topology of closed curves: Some applications in polymer physics ⋮ ALMOST UNKNOTTED EMBEDDINGS OF GRAPHS IN Z³ AND HIGHER DIMENSIONAL ANALOGUES ⋮ Thoughts on lattice knot statistics ⋮ Lattice Polygons and Related Objects ⋮ Monte Carlo Methods for Lattice Polygons ⋮ Entanglement complexity of lattice ribbons ⋮ Mean unknotting times of random knots and embeddings ⋮ Adsorption of lattice polymers with quenched topologies ⋮ Asymptotics of linked polygons ⋮ Asymptotics of multicomponent linked polygons ⋮ Thermodynamic and topological properties of copolymer rings with a segregation/mixing transition

Cites Work

• A spanning tree expansion of the Jones polynomial
• State models and the Jones polynomial
• Jones polynomials and classical conjectures in knot theory
• The minimal number of Seifert circles equals the braid index of a link
• Knots in random walks
• Über eine numerische Knoteninvariante
• Knots and links in spatial graphs
• A polynomial invariant for knots via von Neumann algebras
• Knots in self-avoiding walks
• Statistics of lattice animals
• Polynomials for Links
• Homeomorphic Continuous Curves in 2-Space are Isotopic in 3-Space
• On the Number of Self-Avoiding Walks
• FURTHER RESULTS ON THE RATE OF CONVERGENCE TO THE CONNECTIVE CONSTANT OF THE HYPERCUBICAL LATTICE

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