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.
partitioning boolean lattice into the smallest number of chains
lattice