Computational problems in function theory
Author:
P. A. Morris
Journal:
Math. Comp. 27 (1973), 965971
MSC:
Primary 2004
MathSciNet review:
0338134
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Abstract: In this paper we discuss some computational problems associated with Schurfunctions. A wellknown algorithm for the ordinary product is described and adapted for a computer. A theorem of Todd is discussed in the same way, and these methods are combined to produce a general program for the plethysm (wreath product) of two Sfunctions.
 [1]
P. H. Butler, "Sfunctions and symmetry in physics," J. Physique (Supp. to Nos. 1112) Nov.Dec. 1970, C447 to 49.
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D. B. Hunter, "Analysis of the outer product of symmetric group representations," Nordisk. Tidskr. Informationsbehandling, v. 10, 1970, pp. 106114.
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D.
E. Littlewood, A University Algebra, William Heinemann, Ltd.,
Melbourne, London, Toronto, 1950. MR 0045079
(13,523b)
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D. E. Littlewood, Theory of Group Characters, 2nd ed., Clarendon Press, Oxford, 1950.
 [5]
J. K. S. McKay, "Partitions in natural order (Algorithm 371)," Comm. ACM, v. 13, 1970.
 [6]
P. A. Morris, Graph Theoretic and Computer Applications to Sfunction Theory, Ph.D. Thesis, University of the West Indies, 1970.
 [7]
P.
A. Morris, Applications of graph theory to 𝑆function
theory, J. London Math. Soc. (2) 8 (1974),
63–72. MR
0357216 (50 #9684)
 [8]
Ronald
C. Read, The use of 𝑆functions in combinatorial
analysis, Canad. J. Math. 20 (1968), 808–841.
MR
0229534 (37 #5108)
 [9]
P. R. Smith & B. G. Wybourne, "Plethysm and the theory of complex spectra," J. Mathematical Phys., v. 9, 1968, pp. 10401051.
 [10]
P. R. Smith & B. G. Wybourne, "Selection rules and decomposition of the Kronecker square of irreducible representations," J. Mathematical Phys., v. 8, 1967, pp. 24342440.
 [11]
J.
A. Todd, A note on the algebra of 𝑆functions, Proc.
Cambridge Philos. Soc. 45 (1949), 328–334. MR 0029875
(10,672j)
 [1]
 P. H. Butler, "Sfunctions and symmetry in physics," J. Physique (Supp. to Nos. 1112) Nov.Dec. 1970, C447 to 49.
 [2]
 D. B. Hunter, "Analysis of the outer product of symmetric group representations," Nordisk. Tidskr. Informationsbehandling, v. 10, 1970, pp. 106114.
 [3]
 D. E. Littlewood, A University Algebra, Heinemann, Melbourne, 1950. MR 13, 523. MR 0045079 (13:523b)
 [4]
 D. E. Littlewood, Theory of Group Characters, 2nd ed., Clarendon Press, Oxford, 1950.
 [5]
 J. K. S. McKay, "Partitions in natural order (Algorithm 371)," Comm. ACM, v. 13, 1970.
 [6]
 P. A. Morris, Graph Theoretic and Computer Applications to Sfunction Theory, Ph.D. Thesis, University of the West Indies, 1970.
 [7]
 P. A. Morris, "Applications of graph" theory of Sfunction theory, J. London Math. Soc. (To appear.) MR 0357216 (50:9684)
 [8]
 R. C. Read, "The use of Sfunctions in combinatorial analysis," Canad. J. Math., v. 20, 1968, pp. 808841, MR 37 #5108. MR 0229534 (37:5108)
 [9]
 P. R. Smith & B. G. Wybourne, "Plethysm and the theory of complex spectra," J. Mathematical Phys., v. 9, 1968, pp. 10401051.
 [10]
 P. R. Smith & B. G. Wybourne, "Selection rules and decomposition of the Kronecker square of irreducible representations," J. Mathematical Phys., v. 8, 1967, pp. 24342440.
 [11]
 J. A. Todd, "A note on the algebra of Sfunctions," Proc. Cambridge Philos. Soc., v. 45, 1949, pp. 328334. MR 10, 672. MR 0029875 (10:672j)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197303381344
PII:
S 00255718(1973)03381344
Keywords:
Sfunction,
Schurfunction,
symmetric group,
homogeneous productsum,
symmetric function,
plethysm,
wreath product,
lattice permutation
Article copyright:
© Copyright 1973
American Mathematical Society
