Hasse Diagram of Non-Isomorphic Lattices

[Raghav Gupta]

Homework Statement

There are 15 non-isomorphic lattices on six elements. List them in the form of Hasse diagrams. Among these, identify the seven lattices that are self-dual.

Homework Equations

None required here.

The Attempt at a Solution

Hasse diagram are made to represent a poset( partially ordered set) or a lattice.
Posets are set which follow the relationship of reflexive, anti-symmetric and transitivity on its elements.
Lattice are posets in which every two elements must have a unique least upper bound or unique greatest lower bound.
non - isomorphic lattices are non- similar lattices. Self dual to me in simple terms means when we invert a hasse diagram, it's orientation is same.

In the image below I don't know how the 15 lattices with 6 elements are drawn with logic.

Here I found a link from net.
http://math.chapman.edu/~jipsen/mathposters/lattices7.pdf

 

[nilesh_pat]

In this link you will find all 15 lattices and also the seven self dual lattices.I have described the solution to the best of my knowledge.