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Effect of Negative Control Lines on the Exact Synthesis of Reversible Circuits
Robert Wille, Mathias Soeken, Nils Przigoda and Rolf Drechsler

The main goal of this paper is to classify the fuzzy subgroups of the finite symmetric group Sn . Explicit formulas for the number of distinct fuzzy subgroups of Sn are obtained in the particular cases n = 3 and n = 4. Some inequalities satisfied by this number are also established for n ≥ 5.

MSC (2010): Primary 20N25, 03E72; Secondary 05E15, 20D30, 20D60.

Keywords: Fuzzy subgroups, chains of subgroups, maximal chains of subgroups, symmetric groups, recurrence relations.

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