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European Conference on Computer Algebra

EUROCAL 1985: EUROCAL '85 pp 206–224Cite as

Algorithms for the character theory of the symmetric group

  • Computational Group Theory
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 204))

Abstract

Description of a comprehensive package of routines for the character theory of the symmetric groups Sn have been presented. The efficiency of these algorithms derives from the reduction of the expansions of plethysms and Kronecker products to multiplication of Schur functions. This in turn is done with minimal computational effort by making use of an algorithmic modification of the LR rule due to Remmel and Whitney.

Existing implementations of a number of these algorithms turned out to be very efficient. The calculation of totally symmetric and antisymmetric plethysms for instance, could be carried out further than the existing tables in the literature.

The package is centered around a core which coordinates the various primitives and sequentially invokes the necessary routines to carry out the required calculations. The common features of the various algorithms implemented make it possible to construct this package in a highly modular and compact form in a UNIX environment.

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  1. Department of Computer Science, University of California, 93106, Santa Barbara, CA

    Ömer Eğecioğlu

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  1. Ömer Eğecioğlu
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Bob F. Caviness

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Eğecioğlu, Ö. (1985). Algorithms for the character theory of the symmetric group. In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_267

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  • DOI: https://doi.org/10.1007/3-540-15984-3_267

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