The architecture and Jones polynomials of cycle-crossover polyhedral links

Match

Volumn 63, Issue 3, 2010, Pages 637-656

  Cheng, Xiao Sheng ^a   Zhang, Heping ^a   Hu, Guang ^b   Qiu, Wen Yuan ^b  

^a LANZHOU UNIVERSITY   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953243757     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. J. P. Sauvage, C. D. Buckecker, Molecular Catenaries, Rotaxanes and Knots, Wiley, New York, 1999.
2. C. A. Schalley, Borromean rings: A one-pot synthesis, Angew. Chem. Int. Ed. 43 (2004) 4399-4401.
3. J. S. Siegel, Chemical topology and interlocking molecules, Science 304 (2004) 1256-1258.
4. O. Lukin, F. Vögtle, Knotting and threading of molecules: Chemistry and chirality of molecular knots and their assemblies, Angew. Chem. Int. Ed. 44 (2005) 1456-1477.
5. B. C. Dietrich, B. X. Colasson, J. P. Sauvage, Molecular Knots - In Templates in Chemistry II, Springer, Berlin, 2005.
6. C. D. Pentecost, K. S. Chichak, A. J. Peters, G. W. V. Cave, S. J. Cantrill, J. F. Stoddart, A molecular solomon link, Angew. Chem. Int. Ed. 46 (2007) 218-222.
7. R. P. Goodman, R. M. Berry, A. J. Turberfield, The single-step synthesis of a DNA tetrahedron, Chem Commun. 12 (2004) 1372-1373.
8. R. P. Goodman, I. A. T. Schaap, C. F. Tardin, C. M. Erben, R. M. Berry, C. F. Schmidt, A. J. Turberfield, Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication, Science 310 (2005) 1661-1665.
9. Y. He, T. Ye, M. Su, C. Zhang, A. E. Ribbe, W. Jiang, C. Mao, Hierarchical selfassembly of DNA into symmetric supramolecular polyhedra, Nature 452 (2008) 198-201.
10. J. Chen, N. C. Seeman, Synthesis from DNA of a molecule with the connectivity of a cube, Nature 350 (1991) 631-633.
11. N. C. Seeman, DNA in a material world, Nature 421 (2003) 427-431.
12. C. Zhang, H. K. Seung, M. Su, Y. Leng, E. R. Alexander, W. Jiang and C. Mao, Symmetry controls the face geometry of DNA polyhedra, J. Am. Chem. Soc. 131 (2009) 1413-1415.
13. W. M. Shih, J. D. Quispe, G. F. Joyce, A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron, Nature 427 (2004) 618-621.
14. F. F. Andersen, B. Knudsen, et al., Assembly and structural analysis of a covalently closed nano-scale DNA cage, Nucleic Acids Res. 36 (2008) 1113-1119.
15. Y. Zhang, N. C. Seeman, Construction of a DNA-truncated octahedron, J. Am. Chem. Soc. 116 (1994) 1661-1669.
16. 3h Linkers, Angew. Chem. Int. Ed. 47 (2008) 3626-3630.
17. D. Bhatia, S. Mehtab, R. Krishnan, S. S. Indi, A. Basu, Y. Krishnan, Icosahedral DNA nanocapsules by modular assembly, Angew. Chem. Int. Ed. 48 (2009) 4134-4137.
18. C. Zhang, M. Su, Y. He, X. Zhao, P. A. Fang, E. R. Alexander, W. Jiang, and C. Mao, Conformational flexibility facilitates self-assembly of complex DNA nanostructures, Proc. Natl. Acad. Sci. U. S. A. 105 (2008) 10665-10669.
19. N. Jonoska, R. Twarock, Blueprints for dodecahedral DNA cages, J. Phys. A: Math. Theor. 41 (2008) 304043.
20. W. Y. Qiu, X. D. Zhai, Molecular design of Goldberg polyhedral links, J. Mol. Struct. (Theochem) 756 (2005) 163-166.
21. Y. M. Yang, W. Y. Qiu, Molecular design and mathematical analysis of carbon nanotube links, MATCH Commun. Math. Comput. Chem. 58 (2007) 635-646.
22. X. S. Cheng, W. Y. Qiu, H. P. Zhang, A novel molecular design of polyhedral links and their chiral analysis, MATCH Commun. Math. Comput. Chem. 62 (2009) 115-130.
23. G. Hu, W. Y. Qiu, Extended Goldberg polyhedral links with even tangles, MATCH Commun. Math. Comput. Chem. 61 (2009) 737-752.
24. G. Hu, W. Y. Qiu, Extended Goldberg polyhedral links with even tangles, MATCH Commun. Math. Comput. Chem. 61 (2009) 753-766.
25. W. Y. Qiu, X. D. Zhai, Y. Y. Qiu, Architecture of platonic and archimedean polyhedral links, Sci. China Ser. B51 (2008) 13-18.
26. G. Hu, X. D. Zhai, D. Lu, W. Y. Qiu, The architecture of platonic polyhedral links, J. Math. Chem. 46 (2009) 592-603.
27. T. Kanenobn, T. Sumi, Polynomial invariants of 2-bridge knots through 22 crossings, Math. Comput. 60 (1993) 771-778.
28. R. A. Landvoy, The Jones polynomial of pretzel knots and links, Top. Appl. 83 (1998) 135-147.
29. V. F. R. Jones, Hecke algebra representation of braid groups and link polynomials, Ann. Math. 126 (1987) 335-388.
30. X. A. Jin, F. Zhang, The Kauffman brackets for equivalence classes of links, Adv. Appl. Math. 34 (2005) 47-64.
31. X. A. Jin, F. Zhang, The replacements of signed graphs and Kauffman brackets of link families, Adv. Appl. Math. 39 (2007) 155-172.
32. L. H. Kauffman, A Tutte polynomial for signed graphs, Discr. Appl. Math. 25 (1989) 105-127.
33. L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395-407.
34. L. H. Kauffman, Statistical mechanics and the Jones polynomial, AMS Contemp. Math. Series 78 (1989) 263-297.
35. L. H. Kauffman, New invariants in knot theory, Amer. Math. Monthly 95 (1988) 195-242.
36. R. C. Read, E. G. Whitehead, Chromatic polynomials of homeomorphism classes of graphs, Discr. Math. 204 (1999) 337-356.
37. N. B. Ramsing, T. M. Jovin, Parallel stranded duplex DNA, Nucl. Acids Res. 16 (1988) 6659-6676.
38. V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103-111.
39. C. C. Adams, The Knot Book - An Elementary Introduction to the Mathematical Theory of Knots, Freeman, New York, 1994.