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Original Articles

Applications of multlinear algebra

Pages 211-224 | Published online: 20 Jan 2011

References

  • Balasubramanian , K. 1981 . A method for nuclear spin statistics in molecular spectroscopy . J. Chem. Phys. , 74 : 6824 – 6829 .
  • Balasubramanian , K. 1981 . Generating functions for the nuclear spin statistics of nonrigid molecules . J. Chem. Phys. , 75 : 4572 – 4585 .
  • Balasubramanian , K. 1982 . An algorithm for the generation of nuclear spin species and nuclear spin statistical weights . J. Computational Chem. , 3 : 69 – 74 .
  • Balasubramanian , K. 1982 . Computer generation of nuclear spin species and nuclear spin statistical weights . J. Computational Chem. , 3 : 75 – 88 .
  • Balasubramanian , K. 1985 . Applications of combinatorics and graph theory to spectroscopy and quantum Chemistry . Chem. Rev. , 85 : 599 – 618 .
  • Cvetković , D. M. , Doob , M. and Sachs , H. Spectra of Graphs and
  • Fiedler , M. 1973 . Algebraic connectivity of graphs . Czech Math. J. , 23 : 298 – 305 .
  • Grone , R. and Merris , R. 1988 . A bound for the complexity of a simple graph . Discrete Math. , 69 : 97 – 99 .
  • Grone , R. , Merris , R. and Watkins , W. 1986 . A Hadamard dominance theorem for a class of immanants . Linear and Multilinear Algebra , 19 : 167 – 171 . and
  • James , G. and Kerber , A. 1981 . The Representation Theory of the Symmetric Group , Addison-Wesley .
  • Johnson , C. R. , Merris , R. and Pierce , S. 1985–1986 . Inequalities involving immanants and diagonal products for H-matrices and . Port. Math. , 43 : 43 – 54 .
  • Heyfron , P. 1988 . Immanant dominance orderings for hook partitions . Linear and Multilinear Algebra , 24 : 65 – 78 .
  • Heyfron , P. 1988 . A generalization of Hadamard's inequality . Linear and Multilinear Algebra , 24 to appear
  • Hollas , J. 1987 . Modern Spectroscopy , Wiley .
  • Hunter , D. B. 1983 . The construction of irreducible normalized representations of the general linear group . Linear and Multilinear Algebra , 13 : 357 – 366 .
  • Landau , L. D. and Lifshitz , E. M. 1981 . Quantum Mechanics , Pergamon . 3rd
  • Lieb , E. H. 1966 . Proofs of some conjectures on perrnanents . J. Math. and Mech. , 16 : 127 – 134 .
  • Littlewood , D. E. 1958 . Tlie Theory of Group Characters , Oxford Univ. Press .
  • Macdonald , I. G. 1979 . Symmetric Functions and Hall Polynomials , Clarendon Press .
  • Mckay , B. D. 1977 . On the spectral characteristics of trees . ARS Combinatoria , 3 : 219 – 232 .
  • Marcus , M. and Minc , H. 1965 . Permanents . Amer. Math. Monthly , 72 : 577 – 591 .
  • Merris , R. 1975 . Two problems involving Schur functions . Linear Algebra Appl. , 10 : 155 – 162 .
  • Merris , R. 1978 . The structure of higher degree symmetry classes of tensors II . Linear and Multilinear Algebra , 6 : 171 – 178 .
  • Merris , R. 1980 . Pattern inventories associated with symmetry classes of tensors . Linear Algebra Appl. , 29 : 225 – 230 .
  • Merris , R. 1980 . Manifestations of Polya's counting theorem. . Linear Algebra Appl. , 32 : 209 – 234 .
  • Merris , R. 1983 . Generalized matrix functions and pattern inventory . Linear and Multilinear Algebra , 12 : 315 – 327 .
  • Merris , R. 1983 . Single-hook characters and hamiltonian circuits . linenr and Multilinear Algebra , 14 : 21 – 35 .
  • Merris , R. 1986 . The second immanantal polynomial and the centroid of a graph . SlAM J. Alg. Disc. Meth. , 7 : 484 – 503 .
  • Merris , R. 1987 . “ The permanental dominance conjecture ” . In Current Trends in Matrix Theory , Edited by: Grone , R. and Uhlig , F. 213 – 223 . Elsevier .
  • Merris , R. 1987 . Characteristic vertices of trees . Linear and Multilinear Algebra , 22 : 115 – 131 .
  • Merris , R. 1989 . An edge version of the matrix-tree theorem and the Wiener index . Linear and Multilinear Algebra , 25 : 291 – 296 .
  • Merris , R. 1990 . Tne distance spectrum of a tree . J. Graph Theory , 14 : 365 – 369 .
  • Merris , R. 1991 . Almost all trees are coimmanantal . Linear Algebra Appl. , 150 : 61 – 66 .
  • Merris , R. , Rebman , K. R. and Watkins , W. 1981 . Permanental polynomials of graphs . Linear Algebra Appl. , 38 : 273 – 288 . and
  • Merris , R. and Watkins , W. 1983 . Tensors and graphs . SIAM J. Alg. and Disc. Meth. , 4 : 534 – 547 .
  • Merris , R. and Watkins , W. 1984 . An invariant theory approach to graph enumeration . Linear Algebra Appl. , 61 : 277 – 285 .
  • Mohar , B. 1988 . Eigenvalues, diameter, and mean distance in graphs, Preprint Series . Univ. E. K. Ljubljana , 26 : 317 – 332 .
  • Pate , T. 1991 . Partitions, irreducible characters, and inequalities for generalized matrix functions . Trans. Amer. Math. Soc. , 325 : 875 – 894 .
  • Pate , T. 1990 . Talk at the Auburn Matrix Tlieory Conference
  • Pólya , G. and Read , R. C. 1987 . Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds , Springer-Verlag .
  • Rouvray , D. H. 1986 . Predicting chemistry from topology . Scientific American , 255 Sept. : 40 – 47 .
  • Rudvalis , A. and Snapper , E. 1971 . Numerical polynomials for arbitrary characters . J. Combinatorial Theory , 10 Sept. : 145 – 159 .
  • Stanley , R. 1973 . Acyclic orientations of graphs . Discrete Math , 5 Sept. : 171 – 178 .
  • Wielandt , H. 1967 . “ Topics in the Analytic Theory of Matrices ” . In Lecture Notes prepared by R. Meyer, Math. Dept., Univ , Madison : Wisconsin .
  • Williamson , S. G. 1971 . Operator theoretic invariants and the enumeration theory of Polya and de Bruijn . J. Combinatorial Theory , 11 : 122 – 138 .

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