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A000654 Invertible Boolean functions of n variables.
(Formerly M2173 N0868)
4
1, 2, 52, 142090700, 17844701940501123640681816160, 59757436204078657410908164193971330396709572693816353610758085074676243846093824 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
REFERENCES
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).
LINKS
M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy]
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]
Qing-bin Luo, Jin-zhao Wu, Chen Lin, Computing the Number of the Equivalence Classes for Reversible Logic Functions, Int'l J. of Theor. Phys. (2020) Vol. 59, 2384-2396.
MATHEMATICA
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];
Table[countit[n], {n, 1, 5}] (* Adam P. Goucher, Feb 12 2021 *)
CROSSREFS
Sequence in context: A369089 A216354 A079179 * A061306 A249656 A248987
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Mar 15 2011
STATUS
approved

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Last modified April 20 00:58 EDT 2024. Contains 371798 sequences. (Running on oeis4.)