Invariance groups of finite functions and orbit equivalence of permutation groups

• Autorzy: Eszter K. Horváth , Géza Makay , Reinhard Pöschel , Tamás Waldhauser
• Języki publikacji: EN

Abstrakty

EN

Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections and the corresponding closure operators on Sn, which turn out to provide a generalization of orbit equivalence of permutation groups. We also present some computational results, which show that all primitive groups except for the alternating groups arise as invariance groups of functions defined on a three-element domain.

Słowa kluczowe

EN

Invariance groups; Symmetry groups; Galois connections; Orbit equivalence of permutation groups; Symmetric and alternating groups; Functions of several variables

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

wydano

2015-01-01

otrzymano

2013-07-25

zaakceptowano

2014-07-31

online

2014-10-28

Twórcy

autor

Eszter K. Horváth

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

autor

Géza Makay

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary,

autor

Reinhard Pöschel

• Institut für Algebra, Technische Universität Dresden, D-01062, Dresden, Germany

autor

Tamás Waldhauser

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

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Identyfikatory

DOI

10.1515/math-2015-0010