We show that the Tverberg numberof \mathbb{Z^d and the intersection of convex hulls is required to have a non-empty intersection with S). We determine the m-Tverberg number, when m \geq 3, of any discrete subset S of R^2 (a generalization of an unpublished result of J.-P. Doignon). We also present improvements on } the upper bounds for the Tverberg numbers of Z^3 and Z^j \times R^k  .
This paper discusses Tverberg-type theorems with coordinate constraints (i.e., versions of these theorems where all points lie within a subset S \subset \mathbb{R^d and the intersection of convex hulls is required to have a non-empty intersection with S). We determine the m-Tverberg number, when m \geq 3, of any discrete subset S of R^2 (a generalization of an unpublished result of J.-P. Doignon). We also present improvements on } the upper bounds for the Tverberg numbers of Z^3 and Z^j \times R^k and an integer version of the well-known positive-fraction selection lemma of J. Pach .
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We show that the Tverberg numberof \mathbb{Z
This paper discusses Tverberg-type theorems with coordinate constraints (i.e., versions of these theorems where all points lie within a subset S \subset \mathbb{R
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and an integer version of the well-known positive-fraction selection lemma of J. Pach