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A001532 Number of NP-equivalence classes of self-dual threshold functions of n or fewer variables ; number of majority (i.e., decisive and weighted) games with n players.
(Formerly M0852 N0324)
5
1, 1, 2, 3, 7, 21, 135, 2470, 175428, 52980624 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
H. M. Gurk and J. R. Isbell. 1959. Simple Solutions. In A. W. Tucker and R. D. Luce (eds.) Contributions to the Theory of Games, Volume 4. Princeton, NJ: Princeton University Press, pp. 247-265. (Case n=6.)
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 23. (Cases until n=9.)
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).
J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, New Jersey, 1944. (Cases n=1 to 5.)
LINKS
J.-C. Hausmann, Counting polygon spaces, Boolean functions and majority games, arXiv preprint arXiv:1501.07553 [math.CO], 2015.
J.-C. Hausmann and E. Rodriguez, The space of clouds in Euclidean space, Experiment. Math. 13 (2004), 31-47.
J.-C. Hausmann and E. Rodriguez. The space of clouds in Euclidean space, Corrections and additional material.
J. R. Isbell, On the enumeration of majority games, MTAC, v.13, 1959, pp. 21-28. (Case n=7).
I. Krohn and P. Sudhölter, Directed and weighted majority games, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, row 4, p. 213.
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.
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]
Erik Ordentlich, Ron M. Roth and Gadiel Seroussi, On q-ary Antipodal Matchings and Applications, 2012.
FORMULA
a(n) = Sum_{k=1..n} A003184(k). - Alastair D. King, Oct 26, 2023
CROSSREFS
Sequence in context: A323230 A262305 A189360 * A109456 A155745 A067738
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
a(10) added by W. Lan (wl(AT)fjrtvu.edu.cn), Jun 27 2010
Better description from Alastair King, Mar 17, 2023.
STATUS
approved

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Last modified July 20 15:15 EDT 2024. Contains 374459 sequences. (Running on oeis4.)