R. Merris, Pattern inventories associated with symmetry classes of tensors, Linear Algebra Appl. 29 (1980), 225-230. Research supported by NSF grant MCS 77-28437. Math Reviews 81e: 15015.

Following S. G. Williamson [J. Combinatorial Theory 8 (1970), 162-169; and ibid 11 (1971), 122-138] this article incorporates nonlinear irreducible characters into the theory of combinatorial enumeration developed independently by J. H. Redfield and G. Polya. No doubt it would have merited little more than an asterisk associated with that theory were it not for the theoretical chemist K. Balasubramanian who found the generalization to be just the tool he needed to explain relative amplitudes in Nuclear Magnetic Resonance (NMR) spectroscopy. Details of this application can be found among the following publications of Balasubramanian.

  • The combinatorics of graphical unitary group approach to many electron correlation, Theoretica Chimica Acta 59 (1981), 237-250.
  • A method for nuclear spin statistics in molecular spectroscopy, J. Chem. Phys. 74 (1981), 6824-6829.
  • Generating functions for the nuclear spin statistics of nonrigid molecules, J. Chem. Phys. 75 (1981), 4572-4585.
  • Method for constructing isomerization reactions, Internat'l J. Quantum Chemistry 22 (1982), 385-395.
  • Symmetry operators of generalized wreath products and their applications to chemical physics, Internat'l J. Quantum Chemistry 22 (1982), 1013-1031.
  • An algorithm for the generation of nuclear spin species and nuclear spin statistical weights, J. Computational Chemistry 3 (1982), 69-74.
  • Computer generation of nuclear spin species and nuclear spin statistical weights, J. Computational Chemistry 3 (1982), 75-88.
  • Applications of combinatorics and graph theory to spectroscopy and quantum chemistry, Chem. Rev. 85 (1985), 599-618.
  • Generalization of de Bruijn's extension of Polya's theorem to all characters, J. Math. Chem. 14 (1993), 113-120.

    • Additional publications citing this article are

  • S. Fujita, Bull. Chem. Soc. Japan 72 (1999), 13-20.
  • S. Fujita, Bull. Chem. Soc. Japan 73 (2000), 329-339.
  • K Balasubramanian, Molecular Physics 102 (2004), 659-679.
  • K Balasubramanian, Chemical Physics Letters 391 (2004), 69-74.
  • K Balasubramanian, J. Math. Chem. 35 (2004), 345-365.