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A000654
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Invertible Boolean functions of n variables.
(Formerly M2173 N0868)
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4
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OFFSET
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1,2
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COMMENTS
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Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of permutation and complementation of variables on domain and range. - Sean A. Irvine, Mar 16 2011
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REFERENCES
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M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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cyclify =
Function[{x},
Sort@Tally[Length /@ PermutationCycles[x + 1, Identity]]];
totalweight =
Function[{c}, Product[(x[[1]]^x[[2]]) ( x[[2]]!), {x, c}]];
perms = Function[{n},
Flatten[Table[
FromDigits[Permute[IntegerDigits[BitXor[x, a], 2, n], sigma],
2], {sigma, Permutations[Range[n]]}, {a, 0, 2^n - 1}, {x, 0,
2^n - 1}], 1]];
countit =
Function[{n},
Sum[totalweight[x[[1]]] (x[[2]]^2), {x,
Tally[cyclify /@ perms[n]]}]/((2^n) (n!))^2];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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