<p>As a result of the Dilowrth's theorm we know that the Boolean Lattic can be partitioned into    $\dbinom{n}{n/2}$ chains and it is the smallest number of such chains. Another question regarding that, is who many different possible partitioning of a boolean lattic into smallest chains does exists?
I have some ideas. For example to start from one possible partitioning and find out other possible ones. Please help me with more ideas.</p>

CC BY-SA 3.0
2015-12-19T22:08:43.750Z
Dilworth's theorem says that the size of the largest antichain is equal to the size of the smallest chain partition in *any* poset. The fact you state is a consequence of Dilworth's theorem, and Sperner's lemma.
Sasho Nikolov
CC BY-SA 3.0
2015-12-21T14:43:55.270Z
Like! (not sure that's the term used on the forum, but you know what I mean)
Igor Shinkar
<lattice>
partitioning boolean lattice into the smallest number of chains
user36813
# partitioning boolean lattice into the smallest number of chains

(Asked by: username_0 on 2015-12-19)

As a result of the Dilowrth's theorm we know that the Boolean Lattic can be partitioned into $\dbinom{n}{n/2}$ chains and it is the smallest number of such chains. Another question regarding that, is who many different possible partitioning of a boolean lattic into smallest chains does exists?
I have some ideas. For example to start from one possible partitioning and find out other possible ones. Please help me with more ideas.

**Tags:** lattice
> **Comments:**
> **username_1**: Dilworth's theorem says that the size of the largest antichain is equal to the size of the smallest chain partition in *any* poset. The fact you state is a consequence of Dilworth's theorem, and Sperner's lemma.  
> **username_2**: Like! (not sure that's the term used on the forum, but you know what I mean)  

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