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A001532 Number of self-dual equivalence classes of threshold functions of n or fewer variables, number of majority (i.e., decisive and weighted) games with n players.
(Formerly M0852 N0324)
3
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.)

J.-C. Hausmann and E. Rodriguez. "The space of clouds in Euclidean space". Experiment. Math. 13 (2004), 31-47.

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

Table of n, a(n) for n=1..10.

J.-C. Hausmann, Counting polygon spaces, Boolean functions and majority games, arXiv preprint arXiv:1501.07553, 2015

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).

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, Gadiel Seroussi, On q-ary Antipodal Matchings and Applications, 2012.

CROSSREFS

Sequence in context: A107108 A262305 A189360 * A109456 A155745 A067738

Adjacent sequences:  A001529 A001530 A001531 * A001533 A001534 A001535

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(10) added by W. Lan (wl(AT)fjrtvu.edu.cn), Jun 27 2010

STATUS

approved

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Last modified February 22 15:12 EST 2018. Contains 299454 sequences. (Running on oeis4.)