What do d-complete posets look like?

Any poset P can be decomposed into a disjoint union of its 'connected components,' which are defined in terms of the order diagram of P. So let's restrict our attention to connected d-complete posets.

Here is the order diagram of a typical medium-sized d-complete poset:

Notice that the global structure of this poset is that of a tree. Here and there there appear 'slant irreducible' components which can be thought of as bunches of grapes. (But under certain circumstances, a continuation of the grape vine may occur from an upper corner of a bunch of grapes.)

The order diagram of a d-complete poset may always be embedded in the plane. It is easy to show that a connected d-complete poset has a unique maximal element.

The slant irreducible components of a d-complete poset have been classified.

Move on to a description of the classification of d-complete posets.

Or skip directly to view the various possible slant irreducible components:

First Half of Slant Irreducibles List.

Second Half of Slant Irreducibles List.

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