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On the representation of symmetric polynomials

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J. K. S. McKayAuthors Info & Claims

Communications of the ACM, Volume 10, Issue 7

Pages 428 - 429

https://doi.org/10.1145/363427.363452

Published: 01 July 1967 Publication History

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Abstract

Relations are given between certain symmetric polynomials in the light of the theory of the symmetric group. Such an approach unifies earlier work and lends insight to previously published work by Aaron Booker. A generalization of Graeffe's root-squaring technique for the determination of the roots of a polynomial is suggested.

References

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BOOKER, A. Numerical evaluation of symmetric polynomials. J. ACM 12 (1965), 90-95.

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LITTLEWOOD, D .E . The Theory of Group Characters. Clarendon Press, Oxford, England, 1940.

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ROBINSON, G . DE B . Representation Theory of the Symmetric Group. Edinburgh University Press, Edinburgh, Scotland, 1961.

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MORRIS, A. O. On an algebra of symmetric functions. Quart. J. Math. 16 (1965), 53-64.

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DAVID, F. N., KENDALL, M. G., AND BARTON, D. E. Symmetric Functions and Allied Tables. Cambridge University Press, Cambridge, England, 1966.

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KOSTOVSKII, A.N. A method of numerical solution of algebraic equations with roots of equal modulus. Soviet Math. 1 (1960), 225-228.

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--. The determination of strict inequalities between the moduli of roots in the transformation of algebraic equations by the Lobatchevskii-Graeffe method. Soviet Math. 3 (1962), 1587-1589.

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COM~T, STIG. Calculation of the characters of the symmetric group. Math. Tables Aids Comput. 14, 70 (April, 1960).

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GRAM, C. (ED.) Selected Numerical Methods. Regnecentralen, Copenhagen, 1962.

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McKAY, J. K. S. Algorithm 307. Comm. ACM 10, 7 (July, 1967), 451-452.

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BRATLEY, P., AND McKAY, J. K. S. Algorithm 305. Comm. ACM 10, 7 (July, 1967), 450.

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Cited By

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Eğecioğlu Ö(2005)Algorithms for the character theory of the symmetric groupEUROCAL '8510.1007/3-540-15984-3_267(206-224)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-15984-3_267
McKay JPatera JSharp R(1981)Second and fourth indices of plethysmsJournal of Mathematical Physics10.1063/1.52518322:12(2770-2774)Online publication date: 1-Dec-1981
https://doi.org/10.1063/1.525183
Bratley PMcKay J(1967)Algorithm 305: symmetric polynomialCommunications of the ACM10.1145/363427.36346510:7(450)Online publication date: 1-Jul-1967
https://dl.acm.org/doi/10.1145/363427.363465

Index Terms

On the representation of symmetric polynomials
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Interpolation

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Published In

Communications of the ACM Volume 10, Issue 7

July 1967

79 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/363427

Editor:
Gerard Salton
Cornell Univ., Ithaca, NY

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1967

Published in CACM Volume 10, Issue 7

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Eğecioğlu Ö(2005)Algorithms for the character theory of the symmetric groupEUROCAL '8510.1007/3-540-15984-3_267(206-224)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-15984-3_267
McKay JPatera JSharp R(1981)Second and fourth indices of plethysmsJournal of Mathematical Physics10.1063/1.52518322:12(2770-2774)Online publication date: 1-Dec-1981
https://doi.org/10.1063/1.525183
Bratley PMcKay J(1967)Algorithm 305: symmetric polynomialCommunications of the ACM10.1145/363427.36346510:7(450)Online publication date: 1-Jul-1967
https://dl.acm.org/doi/10.1145/363427.363465

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Abstract

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Recommendations

Wronskian Appell polynomials and symmetric functions

Generalized Bernstein Polynomials and Symmetric Functions

A symmetric sequence of orthogonal polynomials associated with the Stieltjes-Wigert polynomials

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