Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computational problems in $ S$-function theory

Author: P. A. Morris
Journal: Math. Comp. 27 (1973), 965-971
MSC: Primary 20-04
MathSciNet review: 0338134
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • [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,
  • [8] Ronald C. Read, The use of 𝑆-functions in combinatorial analysis, Canad. J. Math. 20 (1968), 808–841. MR 0229534,
  • [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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 20-04

Retrieve articles in all journals with MSC: 20-04

Additional Information

Keywords: S-function, Schur-function, symmetric group, homogeneous productsum, symmetric function, plethysm, wreath product, lattice permutation
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society