The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003183 Number of NPN-equivalence classes of unate Boolean functions of n or fewer variables. (Formerly M0814) 0
 1, 2, 3, 6, 17, 112, 8282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of inequivalent (under the group of permutations and "inversion of variables") monotone Boolean functions of n of fewer variables. Given f, a function of n variables, we define the "inversion of variables", i, by (i.f)(x1,...,xn)=1+f(1+x1,...,1+xn) (we can write (i.f)(x)=1+f(1+x) where the second "1" denotes (1,...,1)). It turns out that if f is monotone, then i.f is also monotone. On the other hand, a permutation of n elements, p, acts on f by (p.f)(x)=f(p(x)). It turns out that if f is monotone, then p.f is also monotone. We define p.i by (p.i)(f)=p.(i.f) and i.p by (i.p)(f)=i.(p.f). If we define a.b by (a.b).f=a.(b.f) for a,b elements of G, it turns out that G={p.i,p: p is a permutation of n elements} is a group. In this context, f and g are equivalent if there exists b (an element of G) such that b.f=g. REFERENCES S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 18. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages] EXAMPLE a(2)=3 because m(x,y)=x,n(x,y)=y,k(x,y)=0,h(x,y)=1,f(x,y)=xy,g(x,y)=x+y+xy are the six monotone Boolean functions of 2 or fewer variables; m and n are equivalent, k and h are equivalent, f and g are equivalent. Then we have 3 inequivalent monotone Boolean functions of 2 or fewer variables. CROSSREFS Cf. A120608, A120587, A006602. Sequence in context: A122939 A321399 A169974 * A213616 A131788 A294455 Adjacent sequences:  A003180 A003181 A003182 * A003184 A003185 A003186 KEYWORD nonn,more AUTHOR EXTENSIONS Additional comments from Alan Veliz-Cuba (alanavc(AT)vt.edu), Jun 18 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)