Computation of Pólya polynomials of primitive permutation groups
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- by Rudolf Land PDF
- Math. Comp. 36 (1981), 267-278 Request permission
Abstract:
An almost complete list of Pólya polynomials of all primitive permutation groups up to degree 20 has been computed. The number-theoretical interpretation of Pólya polynomials and van der Waerden’s test make this a good tool to find safe conjectures for determining the group of an equation. This work was encouraged and supported by Professor W. Jehne, Universität zu Köln.References
- E. Artin, Über die Zetafunktionen gewisser algebraischer Zahlkörper, Math. Ann. 89 (1923), no. 1-2, 147–156 (German). MR 1512140, DOI 10.1007/BF01448095 N. G. de Bruijn, "Pólya’s Abzähl-Theorie: Muster für Graphen und chemische Verbindungen," Selecta Mathematica III (Heidelberger Taschenbücher), v. 86, Springer-Verlag, Heidelberg, 1971, pp. 1-26. J. J. Cannon, A simple language for running group jobs, Tech. Rep., Dept. Pure Math., Univ. of Sydney, 1975.
- A. Hurwitz, Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitutionen seiner Gruppe, Math. Z. 25 (1926), no. 1, 661–675 (German). MR 1544832, DOI 10.1007/BF01283860
- Charles C. Sims, Computational methods in the study of permutation groups, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 169–183. MR 0257203
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 36 (1981), 267-278
- MSC: Primary 20B99; Secondary 12F10, 20-04
- DOI: https://doi.org/10.1090/S0025-5718-1981-0595061-X
- MathSciNet review: 595061