Publications de l’Institut Mathématique, Nouvelle Série, Vol. 100[114], No. 1/1, pp. 95

Publications de l’Institut Mathématique, Nouvelle Série
Vol. 100[114], No. 1/1, pp. 95–99 (2016)

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ON THE NUMBER OF EQUIVALENCE CLASSES OF INVERTIBLE BOOLEAN FUNCTIONS under Action of Permutation of Variables on Domain and Range

Marko Carić, Miodrag Živković

Advanced School of Electrical Engineering Applied Studies, Belgrade, Serbia; Faculty of Mathematics, Department of Informatics, University of Belgrade, Serbia

Abstract: Let $V_{n}$ be the number of equivalence classes of invertible maps from ${0, 1}^{n}$ to ${0, 1}^{n}$ , under action of permutation of variables on domain and range. So far, the values $V_{n}$ have been known for $n \leq 6$ . This paper describes the procedure by which the values of $V_{n}$ are calculated for $n \leq 30$ .

Keywords: invertible Boolean functions; the number of equivalence classes; permutation group

Classification (MSC2000): 05A15; 06E30

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition