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Is there a special term or convenient phrase for the restriction of a convex region to points of a lattice?

This is motivated by wanting to talk about the feasible points of a discrete problem. I'd like to say the points form a convex region, but since they are a subset of the usual integer lattice in several dimensions, that's not AFAIK correct terminology.

I note that convex lattice polytope refers to the (connected) convex region and not to lattice points contained therein.

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    If there were, it would show up in the theory of Ehrhart polynomials (http://en.wikipedia.org/wiki/Ehrhart_polynomial), and I'm not aware of one in that field, so...2012-08-23
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    Yes, I was thinking back over discussions of Pick's Thm. I'd read/heard, and drawing a blank. But at my age(!) that's not best evidence.2012-08-23
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    @MartinSleziak: No offense, but I've rolled back your retagging. The specialized tags don't reflect my topic as well as the broader ones I chose.2012-08-24
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    @hardmath The (lattice) tag is deprecated and [tag:integer-lattices] or [tag:lattice-orders] or [tag:lattices-in-lie-groups] should be used instead (whichever fits). See [meta](http://meta.math.stackexchange.com/questions/1363/tag-merging-and-synonyms/3187#3187) for details. I don't really see the point of creating a new tag called (convex), when we already have [tag:convex-sets].2012-08-24
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    @MartinSleziak: Very well then. Although convex analysis has a substantially more specific meaning than convex sets (and my question is not about analysis), I have rolled back to your tag edits.2012-08-24
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    It was discussed on [meta](http://meta.math.stackexchange.com/questions/1363/tag-merging-and-synonyms/3045#3045) whether [tag:convex-sets] and [tag:convex-analysis] should be made synonyms; it seems that the community consensus was that they should be.2012-08-24
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    @QiaochuYuan: I invite you to post your comment as an answer. Although a "negative" answer, it will be gladly accepted.2012-08-26

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