Journal of Integer Sequences, Vol. 6 (2003), Article 03.1.6

Sequences realized as Parker vectors of oligomorphic permutation groups

Daniele A. Gewurz and Francesca Merola
Dipartimento di Matematica
Università di Roma "La Sapienza"
Piazzale Aldo Moro, 2 -- 00185 Roma
Italy

Abstract: The purpose of this paper is to study the Parker vectors (in fact, sequences) of several known classes of oligomorphic groups. The Parker sequence of a group G is the sequence that counts the number of G-orbits on cycles appearing in elements of G. This work was inspired by Cameron's paper on the sequences realized by counting orbits on k-sets and k-tuples.

(Concerned with sequences A000010 A000005 A000203 A000012 A000007 A019590 A023022 A007395 A054977 A000038 A010701 A000027 A000034 A007425 A023022 A016166 A000079 A002033 A036987 A048298 A002416 A048691 .)

Received October 1, 2002; revised version received April 4, 2003. Published in Journal of Integer Sequences April 15, 2003. Slight revisions, June 11, 2003.