Characteristic monomials with chirality fittingness for combinatorial enumeration of isomers with chiral and achiral ligands

Journal of Chemical Information and Computer Sciences

Volumn 40, Issue 5, 2000, Pages 1101-1112

  Fujita, Shinsaku ^a  

^a KYOTO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142760665     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci000030l     Document Type: Article

References (35)

1. Pólya, G. Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen (Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds). Acta Math. 1937, 68, 145-254.
2. Redfield, J. H. The theory of group-reduced distributions. Am. J. Math. 1927, 49, 433-455.
3. Rouvray, D. H. Isomer enumeration methods. Chem. Soc. Rev. 1974, 3, 355-372.
4. Balaban, A. T. In Chemical Group Theory. Introduction and Fundamentals; Bonchev, D., Rouvray, D. H., Eds.; Gordon & Breach: Laussane, Switzerland, 1994; pp 159-208.
5. Balaban, A. T., Ed. Chemical Applications of Graph Theory; Academic Press: London, 1976.
6. Pólya, G.; Read, R. C. Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds; Springer-Verlag: New York, 1987.
7. Read, R. C. The enumeration of locally restricted graphs (i). J. London Math. Soc. 1959, 34, 417-436.
8. Read, R. C. The enumeration of locally restricted graphs (ii). J. London Math. Soc. 1960, 35, 344-351.
9. Read, R. C. The use of s-functions in combinatorial analysis. Can. J. Math. 1968, 20, 808-841.
10. Foulkes, H. O. On Redfield's group reduction functions. Can. J. Math. 1963, 15, 272-284.
11. Harary, F.; Palmer, E. The enumeration methods of Redfield. Am. J. Math. 1967, 89, 373-384.
12. Davidson, R. A. Isomers and isomerization: Elements of Redfield's combinatorial theory. J. Am. Chem. Soc. 1981, 103, 312-314.
13. Ruch, E.; Hässelbarth, W.; Richter, B. Doppelnebenklassen als Klassenbegriff und Nomenklaturprinzip für Isomere und ihre Abzählung. (Double Cosets as Class Concept and Nomenclature Principle for Isomers and their Enumeration). Theor. Chim. Acta 1970, 19, 288-300.
14. Ruch, E.; Klein, D. J. Double cosets in chemistry and physics. Theor. Chim. Acta 1983, 63, 447-472.
15. Hässelbarth, W. A note on Pólya enumeration theory. Theor. Chim. Acta 1984, 66, 91-110.
16. Hässelbarth, W.; Ruch, E. Isr. J. Chem. 1977, 15, 112.
17. Fujita, S. Subduction of coset representations. An application to enumeration of chemical structures. Theor. Chim. Acta 1989, 76, 247-268.
18. Fujita, S. Symmetry and Combinatorial Enumeration in Chemistry; Springer-Verlag: Berlin-Heidelberg, 1991.
19. Fujita, S. Enumeration of digraphs with a given automorphism group. J. Math. Chem. 1993, 12, 173-195.
20. Fujita, S. Enumeration of chemical structures by subduction of coset representations, correlation of unit subduced cycle indices to Pólya's cycle indices. J. Math. Chem. 1990, 5, 99-120.
21. Fujita, S. Subduction of coset representations. An application to enumeration of chemical structures with achiral and chiral ligands. J. Math. Chem. 1990, 5, 121-156.
22. Fujita, S. Markaracter tables and Q-conjugacy character tables for cyclic subgroups. An application to combinatorial enumeration. Bull. Chem. Soc. Jpn. 1998, 71, 1587-1596.
23. Fujita, S. Maturity of finite groups. An application to combinatorial enumeration of isomers. Bull. Chem. Soc. Jpn. 1998, 71, 2071-2080.
24. Fujita, S. Inherent automorphism and Q-conjugacy character tables of finite groups. An application to combinatorial enumeration of isomers. Bull. Chem. Soc. Jpn. 1998, 71, 2309-2321.
25. Fujita, S. Subduction of Q-conjugacy representations and characteristic monomials for combinatorial enumeration. Theor. Chem. Acc. 1998, 99, 224-230.
26. Fujita, S. Direct subduction of Q-conjugacy representations to give characteristic monomials for combinatorial enumeration. Theor. Chem. Acc. 1998, 99, 404-410.
27. Fujita, S. Characteristic monomial tables for enumeration of achiral and chiral isomers. Bull. Chem. Soc. Jpn. 1999, 72, 13-20.
28. Fujita, S. Chirality fittingness of an orbit governed by a coset representation. Integration of point-group and permutation-group theories to treat local chirality and prochirality. J. Am. Chem. Soc. 1990, 112, 3390-3397.
29. Fujita, S. Generalization of partial cycle indices and modified bisected mark tables for combinatorial enumeration. Bull. Chem. Soc. Jpn. 2000, 73, 329-339.
30. Fujita, S. Möbius function and characteristic monomials for combinatorial enumeration. Theor. Chem. Acc. 1999, 101, 409-420.
31. x/x̃ is used to designate a Q-conjugacy character as well as a Q-conjugacy representation, unless such usage gives confusion.
32. Fujita, S. Promolecules for characterizing stereochemical relationships in nonrigid molecules. Tetrahedron 1991, 47, 31-46.
33. s-column of Table 21.3 (ref 18) should read "2". The corresponding structural formulas have been correctly depicted as structures 53 and 54
34. 3p
35. Fujita, S. Unit subduced cycle indices for combinatorial enumeration. J. Graph Theory 1994, 18, 349-371.