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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 …
Matthieu Latapy's user avatar
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 …
Matthieu Latapy's user avatar
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 …
Matthieu Latapy's user avatar