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Measure partitions using hyperplanes with fixed directions
We study nested partitions of Rd obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partitionExpand
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Helly numbers of algebraic subsets of ℝd and an extension of Doignon’s Theorem
Abstract We study S-convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in ℝd with a proper subset S ⊂ ℝd, and contribute new results about theirExpand
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Line Transversals to Translates of a Convex Body
Let K be a convex body in the plane. Define λ(K,t) as the smallest number satisfying the following: if $\mathcal{F}$ is any family of translates of K such that every t members of $\mathcal{F}$ have aExpand
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A characteristic property of the Euclidean disc
TLDR
In this paper the following is proved: Let K ⊂ $$ \mathbb{E}^2 $$ be a smooth strictly convex body, and let L/K be a line. Expand
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Zero-sum squares in bounded discrepancy {-1,1}-matrices
For $n\ge 5$, we prove that every $n\times n$ $\{-1,1\}$-matrix $M=(a_{ij})$ with discrepancy $\sum a_{ij} \le n$ contains a zero-sum square except for the diagonal matrix (up to symmetries). Here, aExpand
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Lower bounds on geometric Ramsey functions
TLDR
We continue a sequence of recent works studying Ramsey functions for semialgebraic predicates in Rd. Expand
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A Note on the Tolerant Tverberg Theorem
TLDR
We give an asymptotically tight bound for the tolerant Tverberg Theorem when the dimension and the size of the partition are fixed. Expand
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HELLY NUMBERS OF ALGEBRAIC SUBSETS OF R
We study S-convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in R with a proper subset S ⊂ R. We contribute new results about their S-Helly numbers.Expand
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Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of $S$-optimization
The scenario approach developed by Calafiore and Campi to attack chance-constrained convex programs utilizes random sampling on the uncertainty parameter to substitute the original problem with aExpand
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Helly numbers of Algebraic Subsets of $\mathbb R^d$
Author(s): De Loera, J. A.; La Haye, R. N.; Oliveros, D.; Roldan-Pensado, E. | Abstract: We study $S$-convex sets, which are the geometric objects obtained as the intersection of the usual convexExpand
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