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JOURNAL OF
ALGEBRAIC
COMBINATORICS

  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Cycle Action on Treelike Structures

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

DOI: 10.1007/s10801-005-7395-x

Abstract

The purpose of this paper is to study the action on cycles of several known classes of oligomorphic groups, that is, infinite permutation groups of countable degree having only finitely many orbits on k-sets for each k. The groups studied here are all related to trees and treelike relational structures. The sequence whose k-th term is the number of orbits in the action on k-cycles is called Parker sequence. It turns out that, if we are dealing with the automorphism group of a suitable relational structure, this sequence counts also the finite substructures admitting a cyclic automorphism; in calculating these sequences for various groups, we shall thus describe and enumerate such substructures.
Di più dirò: ch'a gli alberi dà vita [I shall say more: the trees are given life spirito uman che sente e che ragiona. by a human spirit that perceives and reasons.

Pages: 105–114

Keywords: keywords oligomorphic permutation groups; action on cycles; circulant relational structures; trees

Full Text: PDF

References

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