Geodesic
Sequences realized as Parker vectors of oligomorphic permutation groups
Journal of integer sequences, Tome 6 (2003) no. 1
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.
Classification : 20B07, 05A15
Keywords: oligomorphic permutation groups, action on cycles, parker vectors, circulant relational structures (Concerned with sequences A023022 
@article{JIS_2003__6_1_a6,
     author = {Gewurz,  Daniele A. and Merola,  Francesca},
     title = {Sequences realized as {Parker} vectors of oligomorphic permutation groups},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {1},
     zbl = {1029.20001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a6/}
}
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Gewurz,  Daniele A.; Merola,  Francesca. Sequences realized as Parker vectors of oligomorphic permutation groups. Journal of integer sequences, Tome 6 (2003) no. 1. http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a6/