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The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
3
votes
Finding a subclass of lattices in the literature
I suggest the following directions, although I am not sure they may help in your specific case.
As you have a list for each $n$, you may consider the sequence defined by their length, and query The O …
2
votes
1
answer
292
views
Objects in bijection with integer partitions (and lattices)
A partition of $n$ is a non-increasing sequence of positive integers of sum $n$. Several lattices are defined over integer partitions, in particular the dominance order and the Young lattice.
Several …
10
votes
Lattices on classical combinatorial families
Lattices are prevalent when one deals with integer partitions.
Let me give a few examples with pictures, that I hope you will enjoy despite the poor quality due to bitmap conversion.
The dominance ord …
2
votes
is there a ‘nice’ lattice on the set of unlabelled graphs with $n$ vertices?
I guess this class is way too small, but since the questions is still unanswered, I will give you an example I like.
An EFG (Edge Firing Game) is defined from an undirected graph $G$ with a distinguis …