- The unknotting number, hard unknot diagrams, and reinforcement learning
2024/09/13 by Taylor Applebaum, Sam Blackwell, Applebaum, Taylor +13 · 1 citation
Computer Science · Mathematics · #57K10 #57K14 #68T07 #68T20 #Artificial Intelligence (cs.AI) #Artificial intelligence #Combinatorics #Computability, Logic, AI Algorithms #Computer science #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #I.2.1 #I.2.6 #I.2.8 #Knot (papermaking) #Machine Learning (cs.LG) #Materials science #Mathematics #Reinforcement learning #Unknot
- On unification of colored annular sl(2) knot homology
2023/05/04 by Anna Beliakova, Beliakova, Anna, Matthew Hogancamp +5 · 2 citations
Mathematics · #57M27 #Algebra over a field #Algebraic structures and combinatorial models #Colored #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Knot (papermaking) #Mathematical analysis #Mathematics #Noncommutative geometry #Orbifold #Physics #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum mechanics #Representation Theory (math.RT) #Uniqueness #Unknot
- New criteria and constructions of Brunnian links
2020/11/01 by Sheng Bai, Weibiao Wang · 1 citation
Computer Science · Mathematics · Neuroscience · Engineering · #Topological and Geometric Data Analysis #Geometric and Algebraic Topology #Motor Control and Adaptation #Unknot #Mathematics #Construct (python library) #Property (philosophy) #Component (thermodynamics) #Link (geometry) #Knot (papermaking) #Theoretical computer science #Pure mathematics #Algebra over a field #Calculus (dental) #Computer science #Combinatorics #Epistemology #Programming language #Engineering
- A polynomial upper bound on Reidemeister moves
2015/07/29 by Marc Lackenby · 2 citations
Mathematics · Computer Science · Engineering · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Unknot #Diagram #Upper and lower bounds #Mathematics #Sequence (biology) #Combinatorics #Polynomial #Mathematical analysis #Knot (papermaking) #Engineering
- Khovanov homology is an unknot-detector
2011/02/10 by P. B. Kronheimer, Tomasz Mrowka · 3 citations
Mathematics · Medicine · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders #Unknot #Khovanov homology #Spectral sequence #Knot (papermaking) #Mathematics #Floer homology #Knot complement #Knot invariant #Pure mathematics #Homology (biology) #Cohomology #Combinatorics #Knot theory #Algebra over a field #Genetics #Biology
- Linkless and flat embeddings in 3-space and the unknot problem
2010/06/13 by Ken‐ichi Kawarabayashi, Stephan Kreutzer, Bojan Mohar · 2 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Geometric and Algebraic Topology #Computational Geometry and Mesh Generation #Unknot #Combinatorics #Embedding #Mathematics #Converse #Book embedding #Disjoint sets #Discrete mathematics #Planar graph #Knot (papermaking) #Graph #Series (stratigraphy) #Chordal graph #1-planar graph #Computer science #Geometry
- Virtual Knot Invariants from Group Biquandles and Their Cocycles
2007/03/20 by J. Scott Carter, Mohamed Elhamdadi, Carter, J. Scott +7 · 2 citations
Computer Science · Engineering · Mathematics · #57M25 #Advanced Combinatorial Mathematics #Braid #Braid group #Braid theory #Checkerboard #Combinatorics #Engineering #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Knot (papermaking) #Knot invariant #Knot theory #Mathematics #Physics #Pure mathematics #Quantum Algebra (math.QA) #Tricolorability #Unknot #math.GT #math.QA #msc:57M25 #semigroups and automata theory
- Arc-presentations of links: Monotonic simplification
2006/01/01 by Ivan Dynnikov · 1 citation
Mathematics · Computer Science · Medicine · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #semigroups and automata theory #Unknot #Monotonic function #Arc (geometry) #Simple (philosophy) #Mathematics #Presentation (obstetrics) #Computer science #Algorithm #Combinatorics #Geometry #Mathematical analysis #Materials science #Medicine #Composite material #Surgery
- A New Way to Represent Links. One-Dimensional Formalism and Untangling Technology
2001/12/01 by I. A. Dynnikov, Ivan Dynnikov · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Braid group #Combinatorics #Commutator subgroup #Geometric and Algebraic Topology #Group (periodic table) #Isotopy #Knot (papermaking) #Mathematics #Normal subgroup #Pure mathematics #Topological and Geometric Data Analysis #Unknot