OFFSET
0,1
COMMENTS
From Fabián Riquelme, Jun 01 2012: (Start)
NP-equivalence classes of threshold functions are equivalent to weighted games, in simple game theory.
The number for n=9 was first documented in Tautenhahn's thesis. (End)
REFERENCES
S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 14.
S. Muroga, T. Tsuboi, and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825.
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).
N. Tautenhahn, Enumeration einfacher Spiele mit Anwendungen in der Stimmgewichtsverteilung, 2008. Master's thesis, University of Bayreuth, 269 pages (in German).
LINKS
S. 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
I. Krohn and P. Sudhölter, Directed and weighted majority games, Math. Methods Operat. Res. 42 (2) (1995) 189-216, Table 1.
S. Kurz, On minimum sum representations for weighted voting games, arXiv:1103.1445 [math.CO], 2011-2018.
S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]
S. Muroga, T. Tsuboi, and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]
Eda Uyanık, Olivier Sobrie, Vincent Mousseau, and Marc Pirlot, Enumerating and categorizing positive Boolean functions separable by a k-additive capacity, Discrete Applied Mathematics, Vol. 229, 1 October 2017, p. 17-30. See Table 3.
FORMULA
a(n) = Sum_{k=0..n} A000619(k). - Alastair D. King, Oct 26, 2023.
CROSSREFS
KEYWORD
nonn,hard,more,nice
AUTHOR
STATUS
approved