# Boolean functions

N. J. A. Sloane njas at research.att.com
Mon Mar 31 18:56:08 CEST 2003

```Gordon Royle was asking about certain definitions

I have always followed the terminilogy in Harrison's book on
"Introduction to Switching and Automata Theory"

A classical B.f. is a map from {0,1}^n to {0,1},
but these were generalized to maps from {0,1}^n to {0,1}^m

An invertible Bf necessarily has m = n

I just now edited the following to make at least
one of these sequences clearer:

%I A000652 M4315 N1807
%S A000652 1,1,6,924,81738720000,256963707943061374889193111552000,
%T A000652 30978254928194376001814792318154658399138184007229852126545533479881553257431040000000
%N A000652 Invertible Boolean functions of n variables.
%C A000652 Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of C_2^n on both domain and range.
%D A000652 M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 154, problem 12.
%D A000652 C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
%F A000652 A000652: n->2^(-2*n)*( (2^n)! + (2^n-1)^2 * ( (2^(n-1))! )*2^(2^(n-1)));
%H A000652 <a href="http://www.research.att.com/~njas/sequences/Sindx_Bo.html#Boolean">Index entries for sequences related to Boolean functions</a>
%K A000652 nonn,easy
%O A000652 0,3
%A A000652 njas
%E A000652 More terms from Vladeta Jovovic (vladeta at Eunet.yu), Feb 23 2000

NJAS

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