A001537 -id:A001537 - cp's OEIS frontend

A000722 Number of invertible Boolean functions of n variables: a(n) = (2^n)!.

1, 2, 24, 40320, 20922789888000, 263130836933693530167218012160000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000

Offset: 0

N. J. A. Sloane

These are invertible maps from {0,1}^n to {0,1}^n, or in other words permutations of the 2^n binary vectors of length n.

2^n-th order derivative of n-th Mandelbrot iterate. Example: a(2) = 24, after one iterate in the Mandelbrot(z(n+1) = z(n)^2 + c) we have the function z(2) = z^4 + 2*c*z^2 + c^2 + c, for which the 4th-order derivative is 24. - Bert van den Bosch (zeusooooo(AT)hotmail.com), Sep 07 2003

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).

Delbert L. Johnson, Table of n, a(n) for n = 0..8
M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
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]
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for sequences related to Boolean functions

Cf. A000652, A000653, A000654, A001038, A001537, A046856, A046857, A244061.

a[n_] := Factorial[2^n]; Table[a[n],{n,0,6}] (* James C. McMahon, Dec 06 2023 *)

atonfact(a,n) = {sr=0; for(x=1,n, y =(a^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) }

a(n) = (2^n)!.

Sum of reciprocals = 0.54169146825401604874... - Cino Hilliard, Feb 08 2003

A000652 Invertible Boolean functions of n variables.

Original entry on oeis.org

1, 1, 6, 924, 81738720000, 256963707943061374889193111552000, 30978254928194376001814792318154658399138184007229852126545533479881553257431040000000

Offset: 0

N. J. A. Sloane

Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of (C_2)^n on both domain and range.

M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 154, problem 12.
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).

M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
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]
Index entries for sequences related to Boolean functions

Cf. A001038, A000653, A000654, A000722, A001537, A046856, A046857.

A000652: n->2^(-2*n)*( (2^n)! + (2^n-1)^2 * ( (2^(n-1))! )*2^(2^(n-1)));

More terms from Vladeta Jovovic, Feb 23 2000

A001038 Invertible Boolean functions with GL(n,2) acting on the domain and range.

Original entry on oeis.org

2, 2, 10, 52246, 2631645209645100680144, 312242081385925594286511113384607360432260178128338777217975928751832

Offset: 1

N. J. A. Sloane

nonn

The Lorens paper gives the incorrect value a(5)=2631645209645100680142. - Sean A. Irvine, Feb 27 2012

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).

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.
Index entries for sequences related to Boolean functions

Cf. A000652, A000653, A000654, A000722, A001537, A046856, A046857.

Corrected and extended by Sean A. Irvine, Feb 26 2012

A128904 Number of AGL(n,2), AGL(n,2) double cosets in S(F_2^n).

Original entry on oeis.org

1, 1, 4, 302, 2569966041123938084

Offset: 1

Marcus Brinkmann (marcus.brinkmann(AT)rub.de), Apr 11 2007

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
Xiang-dong Hou (xhou(AT)euler.math.wright.edu), Affinity of Permutations of F_2^n, Proc. of the Workshop on Coding and Cryptography, pages 273-280, 2003

Index entries for sequences related to Boolean functions

Cf. A001537.

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A000722 Number of invertible Boolean functions of n variables: a(n) = (2^n)!.

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A000652 Invertible Boolean functions of n variables.

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A001038 Invertible Boolean functions with GL(n,2) acting on the domain and range.

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A128904 Number of AGL(n,2), AGL(n,2) double cosets in S(F_2^n).

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