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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 (, and I'm not aware of one in that field, so... – Qiaochu Yuan Aug 23 '12 at 18:25
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. – hardmath Aug 23 '12 at 18:31
@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. – hardmath Aug 24 '12 at 14:40
@hardmath The (lattice) tag is deprecated and integer-lattices or lattice-orders or lattices-in-lie-groups should be used instead (whichever fits). See meta for details. I don't really see the point of creating a new tag called (convex), when we already have convex-sets. – Martin Sleziak Aug 24 '12 at 14:45
@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. – hardmath Aug 24 '12 at 14:56

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