[Cherubino] Quaderni Elettronici del Seminario di Geometria Combinatoria 4E (Aprile 2002), 1--10
Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica

Daniele A. GEWURZ
Parker vectors and cycle indices of permutation groups
(Aprile 2002)

Abstract. In this paper we investigate the relationship between the Parker vector and the cycle index of a permutation group G. We shall show that the former is a kind of compendium of the latter, in the sense that the Parker vector is more concise and can be easily determined (from the cycle index or in other ways) but, on the other hand, usually conveys less information.

Further, we shall prove some ``multiplicative properties" for Parker vectors (that is, their behaviour with respect to direct and wreath products of groups), and compute the Parker vectors of particular groups or families of groups.

Author:
Daniele A. Gewurz
Dipartimento di Matematica pura ed applicata
Università di Padova
Via G. Belzoni 7 - 35151 Padova
e-mail: gewurz@mat.uniroma1.it
The following versions are available: