Invariance groups of functions and related Galois connections-Reference-Cited by-同舟云学术

Invariance groups of functions and related Galois connections

Published:2020-10-23 Issue:2 Volume:62 Page:495-512
ISSN:0138-4821
Container-title:Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
language:en
Short-container-title:Beitr Algebra Geom

Author:

Horváth Eszter K.^ORCID,Pöschel Reinhard^ORCID,Reichard Sven

Abstract

AbstractInvariance groups of sets of Boolean functions can be characterized as Galois closures of a suitable Galois connection. We consider such groups in a much more general context using group actions of an abstract group and arbitrary functions instead of Boolean ones. We characterize the Galois closures for both sides of the corresponding Galois connection and apply the results to known group actions.

Funder

Technische Universität Dresden

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://link.springer.com/content/pdf/10.1007/s13366-020-00525-4.pdf

Reference13 articles.

1. Clote, P., Kranakis, E.: Boolean functions, invariance groups, and parallel complexity. SIAM J. Comput. 20, 553–590 (1991)

2. Dalla Volta, F., Siemons, J.: Permutation groups defined by unordered relations. Ischia Group Theory 2008, pp. 56–67. World Sci. Publ., Hackensack (2009)

3. Grech, M.: Regular symmetric groups of Boolean functions. Discrete Math. 310(21), 2877–2882 (2010)

4. Grech, M., Kisielewicz, A.: Symmetry groups of Boolean functions. Eur. J. Comb. 40, 1–10 (2014)

5. Horváth, E., Makay, G., Pöschel, R., Waldhauser, T.: Invariance groups of finite functions and orbit equivalence of permutation groups. Open Math. 13(1), 83–95 (2015)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Symmetry groups for social preference functions;Mathematical Social Sciences;2024-12

2. Fuzzy relational Galois connections between fuzzy transitive digraphs;Fuzzy Sets and Systems;2023-07

3. Orbit closed permutation groups, relation groups, and simple groups;Journal of Algebraic Combinatorics;2023-01-25