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I've got a copy of Schaum's outline of Discrete Mathematics, and in the section on ordered subsets and lattices, it includes the definition of a consistent enumeration:

Succinctly, given a poset P, there exists f: P -> N, so that if a < b then f(a) < f(b)

http://books.google.com/books?id=6A...meration"&source=gbs_search_s&cad=0#PPA447,M1

However, I had this in my notes that it was not just a function but an injection. Of course, looking at it again, I didn't consider the case of a || b. I don't know where I got this from and now I'm slightly confused. The closest I could find to this definition was a linear extension and topological sorting, which are slightly different.

Does anyone know this topic well enough to dispell my confusion?

Thanks,

- Farley

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# Consistent enumeration on a poset

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