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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (Jan 2015)

Issues

Invariance groups of finite functions and orbit equivalence of permutation groups

Eszter K. Horváth / Géza Makay / Reinhard Pöschel / Tamás Waldhauser
Published Online: 2014-10-28 | DOI: https://doi.org/10.1515/math-2015-0010

Abstract

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.

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

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About the article

Received: 2013-07-25

Accepted: 2014-07-31

Published Online: 2014-10-28

Published in Print: 2015-01-01


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0010.

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© 2015 Eszter K. Horváth et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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