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I have undertaken a project examining lattice model and trying to construct algorithm that could work on all lattice (in physical sense, or crystal structure). I notice there is a branch in mathematics called lattice theory which deals with ordering.

I am wondering whether the lattice theory in mathematics could actually help me in construct such "general algorithm" which can deal with any kinds physical lattice. If so, I will delve into this area. Please help me, thanks.

If you know a more specific mathematical area that deals with general physical lattice ( I have some names in my mind like, mathematical crystallography, lattice graph theory). Please hint me so that I could move forward. Thank you.

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Those are two completely different things, which unfortunately have the same name. See en.wikipedia.org/wiki/Lattice_(group) and en.wikipedia.org/wiki/Lattice_(order). –  Samuel Nov 1 '13 at 20:54
    
It really depends what kind of properties of lattices (in the physical sense) you care about. I should add that lattices in mathematics (ie special types of partially ordered sets) are not related too much with lattices in the physical sense but lattices in the group theoretic sense are related. See en.wikipedia.org/wiki/Lattice_(group). Specifically, they give a way of studying the symmetric behavior of lattice arrangements (ie what kinds of geometric transformations can we apply to the entire lattice). –  Daniel Rust Nov 1 '13 at 20:56
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Begin with math.rwth-aachen.de/~Gabriele.Nebe/LATTICES and book springer.com/mathematics/algebra/book/978-0-387-98585-5 generally referred to as SPLAG –  Will Jagy Nov 1 '13 at 21:34
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Cross-posted to physics.stackexchange.com/q/83130/2451 –  Qmechanic Nov 6 '13 at 1:51
    
Also cross-posted at mathoverflow.net/q/146662/12357 –  Joel Reyes Noche Nov 9 '13 at 0:51

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