Bulletin of the American Mathematical Society

Author(s): Richard P. Stanley
Journal: Bull. Amer. Math. Soc. 1 (1979), 475-511.
MSC (1970): Primary 05-02, 13-02, 20-02, 05A15, 13H10, 20C99
MathSciNet review: 526968
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[A-F]. G. Almkvist and R. Fossum, Decompositions of exterior and symmetric powers of indecomposable Z/pZ-modules in characteristic p and relations to invariants, Københavns Universitet, Matematisk Institut, Preprint Series no. 19, 1977.

[An] G. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications (G.-C. Rota, ed.), vol. 2, Addison-Wesley, Reading, Mass., 1976. MR 557013

[A-M] M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1969. MR 242802

[B-L] W. M. Beynon and G. Lusztig, Some numerical results on the characters of exceptional Weyl groups, Math. Proc. Cambridge Philos. Soc. 84 (1978), 417-426. MR 503002

[B-M-S] E. R. Berlekamp, F. J. MacWilliams and N. J. A. Sloane, Gleason's theorem on self-dual codes, IEEE Trans. Info. Theory 18 (1972), 409-414. MR 335128

[Bo] N. Bourbaki, Groupes et algèbres de Lie, Ch. 4, 5 et 6, Eléments de Mathématique, Fasc. XXXIV, Hermann, Paris, 1968. MR 240238

[dB] N. G. deBruijn, Pólya's theory of counting, Applied Combinatorial Mathematics (E. F. Beckenbach, ed.), Wiley, New York, 1964, pp. 144-184.

[Bu] W. Burnside, Theory of groups of finite order, 2nd ed., Cambridge Univ. Press, 1911; reprinted, Dover, New York, 1955. MR 69818

[Ch] C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 67 (1955), 778-782. MR 72877

[Coh] A. M. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup. 9 (1976), 379-436. MR 422448

[Com] L. Comtet, Advanced combinatorics, Reidel, Dordrecht and Boston, Mass., 1974. MR 460128

[C-R] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Wiley, New York, 1962. MR 144979

[F] L. Flatto, Invariants of finite reflection groups (to appear). MR 519546

[G] B. Gordon, Two theorems on multipartite partitions, J. London Math. Soc. 38 (1963), 459-464. MR 157959

[G-G] A. M. Garsia and I. Gessel, Permutation statistics and partitions, Advances in Math, (to appear). MR 532836

[He] J. C. Hemperly, Problem E2442, Amer. Math. Monthly 80 (1973), 1058; solution, 81 (1974), 1031-1033. MR 1537553

[H-K] J. Herzog and E. Kunz, ed., Der kanonische Modul eines Cohen-Macaulay-rings, Lecture Notes in Math., vol. 238, Springer-Verlag, Berlin, 1971. MR 412177

[Hi] D. Hilbert, Ueber die Theorie der Algebraischen Formen, Math. Ann. 36 (1890), 473-534. MR 1510634

[H-E] M. Hochster and J. A. Eagon, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math. 93 (1971), 1020-1058. MR 302643

[Hu] W. C. Huffman, Polynomial invariants of finite linear groups of degree two (preprint). MR 571926

[I] F. Ischebeck, Eine Dualität zwischen den Funktoren Ext und Tor, J. Algebra 11 (1969), 510-531. MR 237613

[J-B₁] M. V. Jarić and J. L. Birman, New algorithms for the Molien function, J. Math. Physics 18 (1977), 1456-1458. MR 491924

[J-B₂] M. V. Jarić and J. L. Birman, Calculation of the Molien generating function for invariants of space groups, J. Math. Physics 18 (1977), 1459-1464. MR 491926

[Mc] F. J. MacWilliams, A theorem on the distribution of weights in a systematic code, Bell System Tech. J. 42 (1963), 79-84. MR 149978

[M-M-S] F. J. MacWilliams, C. L. Mallows and N. J. A. Sloane, Generalization of Gleason's theorem on weight enumerators of self-dual codes, IEEE Trans. Info. Theory 18 (1972), 794-805. MR 398664

[M-S] C. L. Mallows and N. J. A. Sloane, On the invariants of a linear group of order 336, Proc. Cambridge Philos. Soc. 74 (1973), 435-440. MR 325607

[M-B-D] G. A. Miller, H. F. Blichfeldt and L. E. Dickson, Theory and application of finite groups, Dover, New York, 1961. MR 123600

[Mo] T. Molien, Über die Invarianten der linearen Substitutionsgruppe, Sitzungsber. König. Preuss. Akad. Wiss. (1897), 1152-1156.

[P] G. Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254.

[P-S-W] J. Patera, R. T. Sharp and P. Winternitz, Polynomial irreducible tensors for point groups, J. Math. Phys. 19 (1978), 2362-2376. MR 506710

[Re] J. H. Redfield, The theory of group-reduced distributions, Amer. J. Math. 49 (1927), 433-455. MR 1506633

[Ri] J. Riordan, An introduction to combinatorial analysis, Wiley, New York, 1958. MR 96594

[Ry] H. J. Ryser, Combinatorial mathematics, Carus Math. Monographs, No. 14, Math. Assoc. Amer., Wiley, New York, 1963. MR 150048

[Se₁] J.-P. Serre, Groupes finis d'auomorphisms d'anneaux locaux régulières, Colloq. d'Algèbre, (Paris, 1967), Secrétariat mathématique, Paris, 1968. MR 234953

[Se₂] J.-P. Serre, Algèbre locale-multiplicitiés, Lecture Notes in Math., vol. 11, Springer-Verlag Berlin, 1965. MR 201468

[S-T] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math. 6 (1954), 274-304. MR 59914

[Sl] N. J. A. Sloane, Error-correcting codes and invariant theory: New applications of a nineteenth-century technique, Amer. Math. Monthly 84 (1977), 82-107. MR 424398

[Sm] W. Smoke, Dimension and multiplicity for graded algebras, J. Algebra 21 (1972), 149-173. MR 309920

[So₁] L. Solomon, Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), 57-64. MR 154929

[So₂] L. Solomon, Partition identities and invariants of finite groups, J. Combinatorial Theory Ser. A 23 (1977), 148-175. MR 450382

[Sp₁] T. A. Springer, Regular elements of finite reflection groups, Invent. Math. 25 (1974), 159-198. MR 354894

[Sp₂] T. A. Springer, Invariant theory, Lecture Notes in Math., vol. 585, Springer-Verlag, Berlin, 1977. MR 447428

[Sta₁] R. Stanley, Relative invariants of finite groups generated by pseudo-reflections, J. Algebra 49 (1977), 134-148. MR 460484

[Sta₂] R. Stanley, Hilbert functions of graded algebras, Advances in Math., 28 (1978), 57-83. MR 485835

[Ste] R. Steinberg, Invariants of finite reflection groups, Canad. J. Math. 12 (1960), 616-618. MR 117285

[Str₁] C. W. Strom, On complete systems under certain finite groups, Bull. Amer. Math. Soc. 37 (1931), 570-574.

[Str₂] C. W. Strom, A complete system for the simple group $G_{60}^6$, Bull. Amer. Math. Soc. 43 (1937), 438-440.

[Str₃] C. W. Strom, Complete systems of invariants of the cyclic groups of equal order and degree, Proc. Iowa Acad. Sci. 55 (1948), 287-290. MR 33273

[Wah] J. Wahl, Equations defining rational singularities, Ann. Sci. École Norm. Sup. 10 (1977), 231-264. MR 444655

[Wat₁] K. Watanabe, Certain invariant subrings are Gorenstein. I, Osaka. J. Math. 11 (1974), 1-8. MR 354646

[Wat₂] K. Watanabe, Certain invariant subrings are Gorenstein. II, Osaka J. Math. 11 (1974), 379-388. MR 354646

[We] H. Weyl, The classical groups, 2nd ed., Princeton Univ. Press, Princeton, N. J., 1953. MR 1488158

[Wu] E. M. Wright, Partitions of multi-partite numbers, Proc. Amer. Math. Soc. 7 (1955), 880-890. MR 84012

[Z-S] O. Zariski and P. Samuel, Commutative algebra, vol. II, van Nostrand, Princeton, N. J., 1960. MR 120249

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