Publications de l’Institut Mathématique, Nouvelle Série Vol. 101[115], pp. 99–108 (2017) 

THE CYCLE INDEX OF THE AUTOMORPHISM GROUP OF ${\mathbb{Z}}_{n}$Vladimir Bozovic, Žana Kovijanić VukićevićFaculty of Natural Sciences and Mathematics, University of Montenegro, Podgorica, MontenegroAbstract: We consider the group action of the automorphism group ${I}_{n}=Aut\left({\mathbb{Z}}_{n}\right)$ on the set ${\mathbb{Z}}_{n}$, that is the set of residue classes modulo $n$. Clearly, this group action provides a representation of ${\mathcal{U}}_{n}$ as a permutation group acting on $n$ points. One problem to be solved regarding this group action is to find its cycle index. Once it is found, there appears a vast class of related enumerative and computational problems with interesting applications. We provide the cycle index of specified group action in two ways. One of them is more abstract and hence compact, while another one is basically procedure of composing the cycle index from some building blocks. However, those building blocks are also well explained and finally presented in very detailed fashion. Keywords: cycle index; automorphism group of ${\mathbb{Z}}_{n}$ Classification (MSC2000): 05E99; 20B40;20C40 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.
© 2017 Mathematical Institute of the Serbian Academy of Science and Arts
