Dedekind number

File:Monotone Boolean functions 0,1,2,3.svg|400px|thumb|right|[[File:Loupe light.svg|15px|link=http://upload.wikimedia.org/wikipedia/commons/thumb/5/57/Monotone_Boolean_functions_0%2C1%2C2%2C3.svg/1500px-Monotone_Boolean_functions_0%2C1%2C2%2C3.svg.png]] The free distributive lattices of monotonic Boolean functions on 0, 1, 2, and 3 arguments, with 2, 3, 6, and 20 elements respectively (move mouse over right diagram to see description) circle 659 623 30 [[File:Boolean function 0000 0000.svg|contradiction]] circle 658 552 35 [[File:Boolean functions like 1000 0000.svg|A and B and C]] circle 587 480 35 [[File:Boolean functions like 1000 1000.svg|A and B]] circle 659 481 35 [[File:Boolean functions like 1010 0000.svg|A and C]] circle 729 481 35 [[File:Boolean functions like 1100 0000.svg|B and C]] circle 588 410 35 [[File:Boolean functions like 1010 1000.svg|(A and B) or (A and C)]] circle 658 410 35 [[File:Boolean functions like 1100 1000.svg|(A and B) or (B and C)]] circle 729 410 35 [[File:Boolean functions like 1110 0000.svg|(A and C) or (B and C)]] circle 548 339 30 [[File:Boolean functions like 1010 1010.svg|A]] circle 604 339 30 [[File:Boolean functions like 1100 1100.svg|B]] circle 758 339 30 [[File:Boolean functions like 1111 0000.svg|C]] circle 661 339 35 [[File:Boolean functions like 1110 1000.svg|(A or B) and (A or C) and (B or C) (A and B) or (A and C) or (B and C)]] circle 588 268 35 [[File:Boolean functions like 1110 1010.svg|(A or B) and (A or C)]] circle 659 267 35 [[File:Boolean functions like 1110 1100.svg|(A or B) and (B or C)]] circle 729 268 35 [[File:Boolean functions like 1111 1000.svg|(A or C) and (B or C)]] circle 588 197 35 [[File:Boolean functions like 1110 1110.svg|A or B]] circle 658 197 35 [[File:Boolean functions like 1111 1010.svg|A or C]] circle 729 197 35 [[File:Boolean functions like 1111 1100.svg|B or C]] circle 658 126 35 [[File:Boolean functions like 1111 1110.svg|A or B or C]] circle 659 56 30 [[File:Boolean function 1111 1111.

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Related concepts (2)

Antichain

In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable. The size of the largest antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (totally ordered subsets) into which the set can be partitioned. Dually, the height of the partially ordered set (the length of its longest chain) equals by Mirsky's theorem the minimum number of antichains into which the set can be partitioned.

Distributive lattice

In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to isomorphism—given as such a lattice of sets. As in the case of arbitrary lattices, one can choose to consider a distributive lattice L either as a structure of order theory or of universal algebra.