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1567198
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Book Information:
Author:
G. de B. Robinson
Title:
The collected papers of Alfred Young
Additional book information:
University of Toronto Press, Toronto and Buffalo, 1977, xxvii + 684 pp., $10.00.
G. E. Baird and L. C. Biedenharn, On the representations of the semisimple Lie groups. II, J. Mathematical Phys. 4 (1963), 1449–1466. MR 156922, DOI 10.1063/1.1703926
F. N. David and D. E. Barton, Combinatorial chance, Hafner Publishing Co., New York, 1962. MR 0155371
D. E. Barton and C. L. Mallows, Some aspects of the random sequence, Ann. Math. Statist. 36 (1965), 236–260. MR 178488, DOI 10.1214/aoms/1177700286
Johan G. F. Belinfante and Bernard Kolman, A survey of Lie groups and Lie algebras with applications and computational methods, Classics in Applied Mathematics, vol. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989. Reprint of the 1972 original. MR 1015710, DOI 10.1137/1.9781611971330
Mark Benard, On the Schur indices of characters of the exceptional Weyl groups, Ann. of Math. (2) 94 (1971), 89–107. MR 297887, DOI 10.2307/1970736
Mark Benard, Schur indices and splitting fields of the unitary reflection groups, J. Algebra 38 (1976), no. 2, 318–342. MR 401901, DOI 10.1016/0021-8693(76)90223-4
C. T. Benson and L. C. Grove, The Schur indices of the reflection group ${\cal I}_{4}$, J. Algebra 27 (1973), 574–578. MR 327881, DOI 10.1016/0021-8693(73)90065-3
C. Berge, Principes de combinatoire, Dunod, Paris, 1968 (French). MR 0237346
L. C. Biedenharn and J. D. Louck, Angular momentum in quantum physics, Encyclopedia of Mathematics and its Applications, vol. 8, Addison-Wesley Publishing Co., Reading, Mass., 1981. Theory and application; With a foreword by Peter A. Carruthers. MR 635121
William H. Burge, Four correspondences between graphs and generalized Young tableaux, J. Combinatorial Theory Ser. A 17 (1974), 12–30. MR 351884, DOI 10.1016/0097-3165(74)90024-7
11. H.-T. Chen, Collective motions of the isospin degrees of freedom of a system of paired nucleons, Nuclear Phys. A 212 (1973), 317-340.
Joan E. Herman and Fan R. K. Chung, Some results on hook lengths, Discrete Math. 20 (1977/78), no. 1, 33–40. MR 463279, DOI 10.1016/0012-365X(77)90040-1
Jean A. Dieudonné and James B. Carrell, Invariant theory, old and new, Academic Press, New York-London, 1971. MR 0279102
R. Elazar and M. Gutterman, On a problem of random walk in space, Canad. Math. Bull. 14 (1971), 503–506. MR 368098, DOI 10.4153/CMB-1971-090-4
P. Erdös and G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463–470. MR 1556929
16. M. B. Faist, Angular entropy: the information content of molecular scattering angular distributions, J. Chem. Phys. 66 (1977), 511-523.
Charles S. Fisher, The death of a mathematical theory. A study in the sociology of knowledge, Arch. History Exact Sci. 3 (1966), 137–159 (1966). MR 0202546, DOI 10.1007/BF00357267
Dominique Foata, Une propriété du vidage-remplissage des tableaux de Young, Combinatoire et représentation du groupe symétrique (Actes#Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 121–135 (French). MR 0466293
Dominique Foata, Une propriété du vidage-remplissage des tableaux de Young, Combinatoire et représentation du groupe symétrique (Actes#Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 121–135 (French). MR 0466293
H. O. Foulkes, Paths in ordered structures of partitions, Discrete Math. 9 (1974), 365–374. MR 387071, DOI 10.1016/0012-365X(74)90083-1
H. O. Foulkes, Irreducible matrix representations of certain finite groups, J. London Math. Soc. 21 (1946), 226–233. MR 20080, DOI 10.1112/jlms/s1-21.3.226
H. O. Foulkes, Recurrences for characters of the symmetric group, Discrete Math. 21 (1978), no. 2, 137–144. MR 523061, DOI 10.1016/0012-365X(78)90086-9
J. S. Frame, G. de B. Robinson, and R. M. Thrall, The hook graphs of the symmetric groups, Canad. J. Math. 6 (1954), 316–324. MR 62127, DOI 10.4153/cjm-1954-030-1
24. G. Frobenius, Über die charakteristischen Einheiten der symmätrischen Gruppe, Berliner Sitzungsberichte (1903), 328-358 (also, Gesammelte Abhandlungen, vol. 3, Springer-Verlag, Berlin, 1968, pp. 244-274).
25. G. Frobenius, Gesammelte Abhandlungen, 3 vols., Springer-Verlag Berlin and New York, 1968.
A. M. Garsia and J. Remmel, On the raising operators of Alfred Young, Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978) Proc. Sympos. Pure Math., XXXIV, Amer. Math. Soc., Providence, R.I., 1979, pp. 181–198. MR 525327
A. M. Garsia and J. Remmel, Symmetric functions and raising operators, Linear and Multilinear Algebra 10 (1981), no. 1, 15–23. MR 615022, DOI 10.1080/03081088108817389
28. J. H. Grace and A. Young, The algebra of invariants, Cambridge Univ. Press, London, 1903 (reprinted: Chelsea, New York).
Curtis Greene, An extension of Schensted’s theorem, Advances in Math. 14 (1974), 254–265. MR 354395, DOI 10.1016/0001-8708(74)90031-0
Curtis Greene, Some partitions associated with a partially ordered set, J. Combinatorial Theory Ser. A 20 (1976), no. 1, 69–79. MR 398912, DOI 10.1016/0097-3165(76)90078-9
Curtis Greene, Some order-theoretic properties of the Robinson-Schensted correspondence, Combinatoire et représentation du groupe symétrique (Actes Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 114–120. MR 0462965
Larry C. Grove, The characters of the hecatonicosahedroidal group, J. Reine Angew. Math. 265 (1974), 160–169. MR 330275, DOI 10.1515/crll.1974.265.160
Thomas Hawkins, Hypercomplex numbers, lie groups, and the creation of group representation theory, Arch. History Exact Sci. 8 (1972), no. 4, 243–287. MR 1554156, DOI 10.1007/BF00328434
34. P. Hoefsmit, Representations of generic algebras corresponding to classical Weyl groups, Notices Amer. Math. Soc. 23 (1976), A297-A298.
David Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890), no. 4, 473–534 (German). MR 1510634, DOI 10.1007/BF01208503
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37. A. P. Hillman and R. M. Grassl, Tableaux enumeration and Wronskians, Notices Amer. Math. Soc. 23 (1976), A674.
38. A. P. Hillman and R. M. Grassl, Functions on tableau frames, Notices Amer. Math. Soc. 24 (1977), A636.
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D. B. Hunter, The reduction of a direct product of induced matrices, Quart. J. Math. Oxford Ser. (2) 19 (1968), 81–87. MR 222098, DOI 10.1093/qmath/19.1.81
D. B. Hunter, Unitary representations of the unitary group, Proc. Cambridge Philos. Soc. 65 (1969), 377–386. MR 236281, DOI 10.1017/s0305004100044352
G. D. James, Representations of the symmetric groups over the field of order $2$, J. Algebra 38 (1976), no. 2, 280–308. MR 396734, DOI 10.1016/0021-8693(76)90220-9
G. D. James, The irreducible representations of the symmetric groups, Bull. London Math. Soc. 8 (1976), no. 3, 229–232. MR 417272, DOI 10.1112/blms/8.3.229
G. D. James, On the decomposition matrices of the symmetric groups. I, J. Algebra 43 (1976), no. 1, 42–44. MR 430049, DOI 10.1016/0021-8693(76)90142-3
G. D. James, On the decomposition matrices of the symmetric groups. I, J. Algebra 43 (1976), no. 1, 42–44. MR 430049, DOI 10.1016/0021-8693(76)90142-3
G. D. James, A characteristic-free approach to the representation theory of ${\mathfrak {S}}_{n}$, J. Algebra 46 (1977), no. 2, 430–450. MR 439924, DOI 10.1016/0021-8693(77)90380-5
G. D. James, Some combinatorial results involving Young diagrams, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 1–10. MR 463280, DOI 10.1017/S0305004100054220
G. D. James, On a conjecture of Carter concerning irreducible Specht modules, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 11–17. MR 463281, DOI 10.1017/S0305004100054232
G. D. James, The representation theory of the symmetric groups, Lecture Notes in Mathematics, vol. 682, Springer, Berlin, 1978. MR 513828
52. A. Kerber, On a connection between the representation theories of symmetric groups and general finite groups, Proceedings of the Alfred Young Day Conference, Waterloo, 1978.
Donald E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific J. Math. 34 (1970), 709–727. MR 272654
Donald Knutson, $\lambda$-rings and the representation theory of the symmetric group, Lecture Notes in Mathematics, Vol. 308, Springer-Verlag, Berlin-New York, 1973. MR 0364425
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57. G. Kreweras, Traitement simultané du "problème de Young" et du "problème de Simon Newcomb", Cahiers du B. U. R. O., No. 10, Paris, 1967.
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Bernhard Lesche, A theorem on Ruch’s principle of nonequilibrium statistics, J. Mathematical Phys. 17 (1976), no. 3, 427–430. MR 403520, DOI 10.1063/1.522911
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D. E. Littlewood, A university algebra, Dover Publications, Inc., New York, 1970. An introduction to classic and modern algebra; Republication of the second (1958) edition. MR 0345745
66. D. E. Littlewood, The skeleton key of mathematics, Hutchinson Univ. Library, London, 1960 (Reprinted in French translation: Le passe-partout mathématique, Masson et Cie, Paris, 1964).
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68. I. G. Macdonald, Symmetric functions and Hall polynomials (to appear).
Percy Alexander MacMahon, Collected papers. Vol. I, Mathematicians of Our Time, MIT Press, Cambridge, Mass.-London, 1978. Combinatorics; Edited and with a preface by George E. Andrews; With an introduction by Gian-Carlo Rota. MR 514405
A. O. Morris, Projective representations of Abelian groups, J. London Math. Soc. (2) 7 (1973), 235–238. MR 327885, DOI 10.1112/jlms/s2-7.2.235
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A. O. Morris, Projective representations of reflection groups, Proc. London Math. Soc. (3) 32 (1976), no. 3, 403–420. MR 486086, DOI 10.1112/plms/s3-32.3.403
David Mumford, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 34, Springer-Verlag, Berlin-New York, 1965. MR 0214602
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T. V. Narayana, A partial order and its applications to probability theory, Sankhyā 21 (1959), 91–98. MR 106498
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Gilbert de B. Robinson, The papers of Alfred Young (1873–1940), Combinatoire et représentation du groupe symétrique (Actes Table Ronde C.N.R.S., Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 11–28. MR 0437276
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J. Désarménien, Joseph P. S. Kung, and Gian-Carlo Rota, Invariant theory, Young bitableaux, and combinatorics, Advances in Math. 27 (1978), no. 1, 63–92. MR 485944, DOI 10.1016/0001-8708(78)90077-4
97. E. Ruch and A. Schönhofer, Theorie der Chiralitätsfunktionen, Theoret. Chim. Acta (Berlin) 19 (1970), 225-287.
Ernst Ruch, The diagram lattice as structural principle, Theoret. Chim. Acta 38 (1975), no. 3, 167–183. MR 503057, DOI 10.1007/BF01125896
99. E. Ruch and A. Mead, The principle of increasing mixing character and some of its consequences, Theoret. Chim. Acta (Berlin) 41 (1976), 95-117.
Daniel Edwin Rutherford, Substitutional Analysis, Edinburgh, at the University Press, 1948. MR 0027272
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Glânffrwd P. Thomas, Further results on Baxter sequences and generalized Schur functions, Combinatoire et représentation du groupe symétrique (Actes Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 155–167. MR 0472546
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- 31.
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Review Information:
Reviewer:
George E. Andrews
Journal:
Bull. Amer. Math. Soc.
1 (1979), 989-997
DOI:
https://doi.org/10.1090/S0273-0979-1979-14710-4