# What is a Lattice?

To be up front, I was helping my friend with his programming assignment and I stumbled upon the following sentence

List all the lattices (subsets of S) on S with size K

it later says that the partial order is defined as "is multiple of"

I don't quite understand what this means. Can someone explain the theory behind this?

I checked on wikipedia but there is a lot of jargon that I don't understand. Any assistance with this would be appreciated.

I should note that my mathematics is not the strongest.

• What does your friend's textbook or class notes have to say about lattices? If it were me and I didn't know the term, and if I also thought I could still be of assistance, I would ask to look at these. However, I suspect I would probably just say "sorry, I don't know anything about lattices, so I don't think I can be of any help". That said, maybe some of the results from a google search for "lattice" {AND} "discrete mathematics" could help. Commented Oct 20, 2014 at 21:33