A132183 Number of "regular" Boolean functions of n variables.

2, 3, 5, 10, 27, 119, 1173, 44315, 16175190, 284432730176

Offset: 0

Author

Don Knuth, Nov 19 2007

Keywords

• nonn
• more

Comments

The sequence also counts order ideals (or antichains) of the binary majorization lattice with 2^n points. That lattice for n=5 will be illustrated in Fig. 8 of Volume 4 of The Art of Computer Programming. The basic properties of this lattice will be discussed in exercise 7.1.1-109 of that book. (The material of Section 7.1.1 will be available in paperback in a couple months.)

Michael Somos (Mar 13 2012) asks if A003187 and A132187 are the same. - N. J. A. Sloane, Mar 13 2012

For n from 1 to 8, a(n) agrees with the number of directed games on n players in Table 1 of Krohn and Sudhölter. - Peter Bala, Dec 16 2021

Examples

			For example, the 10 Boolean functions for n=3 have the truth tables
  00000000
  00000001
  00000011
  00000111
  00001111
  00010111
  00011111
  00111111
  01111111
  11111111
(things don't get very interesting until n=4 or 5).
		

Links

• Stefan Bolus, A QOBDD-based Approach to Simple Games, Dissertation, Doktor der Ingenieurwissenschaften der Technischen Fakultaet der Christian-Albrechts-Universitaet zu Kiel, 2012. - From _N. J. A. Sloane_, Dec 22 2012
• Bjørn Kjos-Hanssen, Lei Liu, The number of languages with maximum state complexity, arXiv:1902.00815 [cs.FL], 2019.
• I. Krohn and P. Sudhölter, Directed and weighted majority games, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, row 1, p. 213; also on ResearchGate.

Crossrefs

Cf. A003187.