

A006602


Number of hierarchical models with linear terms forced.
(Formerly M1532)


10




OFFSET

0,1


COMMENTS

Also number of pure (= irreducible) grouptesting histories of n items  A. Boneh, Mar 31 2000
Also number of antichain covers of an unlabeled nset, so a(n) equals first differences of A003182.  Vladeta Jovovic, Goran Kilibarda, Aug 18 2000
Also number of inequivalent (under permutation of variables) nondegenerate monotone Boolean functions of n variables. We say h and g (functions of n variables) are equivalent if there exists a permutation p of S_n such that hp=g. E.g., a(3)=5 because xyz, xy+xz+yz, x+yz+xyz, xy+xz+xyz, x+y+z+xy+xz+yz+xyz are 5 inequivalent nondegenerate monotone Boolean functions that generate (by permutation of variables) the other 4. For example, y+xz+xyz can be obtained from x+yz+xyz by exchanging x and y.  Alan VelizCuba (alanavc(AT)vt.edu), Jun 16 2006


REFERENCES

Y. M. M. Bishop, S. E. Fienberg and P. W. Holland, Discrete Multivariate Analysis. MIT Press, 1975, p. 34.
V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
A. A. Mcintosh, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..7.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
C. Lienkaemper, When do neural codes come from convex or good covers?, 2015.
C. L. Mallows, Emails to N. J. A. Sloane, JunJul 1991


FORMULA

a(n) = A007411(n)+1.


CROSSREFS

Cf. A006126 (labeled case), A007411.
Sequence in context: A031148 A032238 A000619 * A144824 A144358 A049404
Adjacent sequences: A006599 A006600 A006601 * A006603 A006604 A006605


KEYWORD

nonn,nice,hard


AUTHOR

Colin Mallows


EXTENSIONS

a(6) from A. Boneh, 32 Hantkeh St., Haifa 34608, Israel, Mar 31 2000
Entry revised by N. J. A. Sloane, Jul 23 2006
a(7) from A007411 and A003182.  N. J. A. Sloane, Aug 13 2015


STATUS

approved



