Computational problems in -function theory

Author:
P. A. Morris

Journal:
Math. Comp. **27** (1973), 965-971

MSC:
Primary 20-04

DOI:
https://doi.org/10.1090/S0025-5718-1973-0338134-4

MathSciNet review:
0338134

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we discuss some computational problems associated with Schur-functions. A well-known 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 *S*-functions.

**[1]**P. H. Butler, "*S*-functions and symmetry in physics,"*J. Physique*(Supp. to Nos. 11-12) Nov.-Dec. 1970, C4-47 to 49.**[2]**D. B. Hunter, "Analysis of the outer product of symmetric group representations,"*Nordisk. Tidskr. Informationsbehandling*, v. 10, 1970, pp. 106-114.**[3]**D. E. Littlewood,*A University Algebra*, William Heinemann, Ltd., Melbourne, London, Toronto, 1950. MR**0045079****[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 S-function Theory*, Ph.D. Thesis, University of the West Indies, 1970.**[7]**P. A. Morris,*Applications of graph theory to 𝑆-function theory*, J. London Math. Soc. (2)**8**(1974), 63–72. MR**0357216**, https://doi.org/10.1112/jlms/s2-8.1.63**[8]**Ronald C. Read,*The use of 𝑆-functions in combinatorial analysis*, Canad. J. Math.**20**(1968), 808–841. MR**0229534**, https://doi.org/10.4153/CJM-1968-080-x**[9]**P. R. Smith & B. G. Wybourne, "Plethysm and the theory of complex spectra,"*J. Mathematical Phys.*, v. 9, 1968, pp. 1040-1051.**[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. 2434-2440.**[11]**J. A. Todd,*A note on the algebra of 𝑆-functions*, Proc. Cambridge Philos. Soc.**45**(1949), 328–334. MR**0029875**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0338134-4

Keywords:
*S*-function,
Schur-function,
symmetric group,
homogeneous productsum,
symmetric function,
plethysm,
wreath product,
lattice permutation

Article copyright:
© Copyright 1973
American Mathematical Society