1,2

An antichain cover is a cover such that no element of the cover is a subset of another element of the cover.

Also, the number of nondegenerate monotone boolean functions of n variables in an n-variable boolean algebra. - Rodrigo A. Obando (R.Obando(AT)computer.org), Jul 26 2004

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 the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)

V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

C. L. Mallows (colinm(AT)research.avayalabs.com), personal communication.

A. A. Mcintosh, personal communication.

R. A. Obando, On the number of nondegenerate monotone boolean functions of n variables, In Preparation.

K. S. Brown, Dedekind's problem

R. A. Obando, Project: A Map of a Rule Space (To be posted).

Eric Weisstein's World of Mathematics, Antichain covers"

a(n)=Sum_{k=1..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of k-antichain covers of a labeled n-set.

a(5)=1+90+790+1895+2116+1375+490+115+20+2=6894.

There are 9 antichain covers of a labeled 3-set: {{1,2,3}}, {{1},{2,3}}, {{2},{1,3}}, {{3},{1,2}}, {{1,2},{1,3}}, {{1,2},{2,3}}, {{1,3},{2,3}}, {{1},{2},{3}}, {{1,2},{1,3},{2,3}}.

Cf. A000372, A056046-A056049, A056052, A056101, A056104, A051112-A051118.

Sequence in context: A062498 A008269 A039718 this_sequence A075538 A067965 A135543

Adjacent sequences: A006123 A006124 A006125 this_sequence A006127 A006128 A006129

nonn,nice,hard

njas

Last 3 terms from Michael Bulmer (mrb(AT)maths.uq.edu.au)

Antichain interpretation from Vladeta Jovovic and Goran Kilibarda (vladeta(AT)Eunet.yu), Jul 31 2000