Symmetry and Combinatorial Enumeration in Chemistry

1. Front Matter

   Pages I-IX

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2. Introduction

   • Shinsaku Fujita

   Pages 1-6

3. Symmetry and Point Groups

   • Shinsaku Fujita

   Pages 7-15

4. Permutation Groups

   • Shinsaku Fujita

   Pages 17-27

5. Axioms and Theorems of Group Theory

   • Shinsaku Fujita

   Pages 29-43

6. Coset Representations and Orbits

   • Shinsaku Fujita

   Pages 45-61

7. Systematic Classification of Molecular Symmetries

   • Shinsaku Fujita

   Pages 63-73

8. Local Symmetries and Forbidden Coset Representations

   • Shinsaku Fujita

   Pages 75-87

9. Chirality Fittingness of an Orbit

   • Shinsaku Fujita

   Pages 89-100

10. Subduction of Coset Representations

    • Shinsaku Fujita

    Pages 101-115

11. Prochirality

    • Shinsaku Fujita

    Pages 117-133

12. Desymmetrization of Para-Achiral Compounds

    • Shinsaku Fujita

    Pages 135-145

13. Topicity and Stereogenicity

    • Shinsaku Fujita

    Pages 147-161

14. Counting Orbits

    • Shinsaku Fujita

    Pages 163-179

15. Obligatory Minimum Valencies

    • Shinsaku Fujita

    Pages 181-195

16. Compounds with Achiral Ligands Only

    • Shinsaku Fujita

    Pages 197-213

17. New Cycle Index

    • Shinsaku Fujita

    Pages 215-225

18. Cage-Shaped Molecules with High Symmetries

    • Shinsaku Fujita

    Pages 227-240

19. Elementary Superposition

    • Shinsaku Fujita

    Pages 241-253

20. Compounds with Achiral and Chiral Ligands

    • Shinsaku Fujita

    Pages 255-270

This book is written to introduce a new approach to stereochemical problems and to combinatorial enumerations in chemistry. This approach is based on group the­ ory, but different from conventional ways adopted by most textbooks on chemical group theory. The difference sterns from their starting points: conjugate subgroups and conjugacy classes. The conventional textbooks deal with linear representations and character ta­ bles of point groups. This fact implies that they lay stress on conjugacy classesj in fact, such group characters are determined for the respective conjugacy classes. This approach is versatile, since conjugacy classes can be easily obtained by ex­ amining every element of a group. It is unnecessary to know the group-subgroup relationship of the group, which is not always easy to obtain. The same situa­ tion is true for chemical enumerations, though these are founded on permutation groups. Thus, the P6lya-Redfield theorem (1935 and 1927) uses a cycle index that is composed of terms associated with conjugacy classes.

• Cycle index
• Gruppentheorie
• Lattice
• Permutation
• Polya
• Stereochemie
• Topicity
• chemistry
• chirality
• classification
• fields
• molecule
• skeleton
• stereochemistry
• synthesis
• combinatorics

• Research Laboratories, Ashigara, Fuji Photo Film Co., Ltd., Minami-Ashigara, Kanagawaken, Japan

  Shinsaku Fujita

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