Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

Computation of Pólya polynomials of primitive permutation groups


Author: Rudolf Land
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [1] E. Artin, Über die Zetafunktionen gewisser algebraischer Zahlkörper, Math. Ann. 89 (1923), no. 1-2, 147–156 (German). MR 1512140, https://doi.org/10.1007/BF01448095
  • [2] 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.
  • [3] J. J. Cannon, A simple language for running group jobs, Tech. Rep., Dept. Pure Math., Univ. of Sydney, 1975.
  • [4] 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, https://doi.org/10.1007/BF01283860
  • [5] 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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 20B99, 12F10, 20-04

Retrieve articles in all journals with MSC: 20B99, 12F10, 20-04


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0595061-X
Article copyright: © Copyright 1981 American Mathematical Society