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An integrally-convex set is the discrete geometry analogue of the concept of convex set in geometry.
A subset X of the integer grid Z n {\displaystyle \mathbb {Z} ^{n}} is integrally convex if any point y in the convex hull of X can be expressed as a convex combination of the points of X that are "near" y, where "near" means that the distance between each two coordinates is less than 1.
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