On Kemnitz’ conjecture concerning lattice-points in the plane
By Christian Reiher. 2007
96 citations recorded by the source corpus.
In 1961, Erdős, Ginzburg and Ziv proved a remarkable theorem stating that each set of 2n−1 integers contains a subset of size n, the sum of whose elements is divisible by n. We will prove a similar result for pairs of integers, i.e. planar lattice-points, usually referred to as Kemnitz’ conjecture.
Subfields: Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/e65301173704e0e8f8563cfc0b0a1414d8038199
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In Computer Graphics and Computer-Aided Design
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Citations in the corpus
- Zero-sum problems in finite abelian groups and affine caps (2006, background): “It contains the result by Reiher [56], which states that s(Cp ⊕ Cp) = 4p − 3 for all p ∈ P [56, 59], and it contains the theorem of Erdős, Ginzburg and Ziv (set n1 = 1; see [19] for the original paper; for various proofs see [1; 51, section 2.”
- Inverse zero-sum problems II (2008, background): “(G), and for s(G) in the cyclic case, are classical (see [9, 23, 28]), yet the results on s(G) and s exp(G)N(G) for groups of rank two were obtained only recently (see [20, Theorem 5.8.3] building on [24, 25] and [14, Theorem 6.5], respectively). INVERSE ZERO-SUM PROBLEMS II 7 Theorem4.1.Let m,n∈ Na”
- Inverse zero-sum problems III (2008, background): “Proof. The result on D(G) goes back to D. Kruyswijk and J. E. Olson, and the result on s(G) is based on C. Reiher’s result that s(Cp ⊕Cp) = 4p−3 (see [ 35 ] and [30, Theorem 5.8.3]).”
- Inverse zero-sum problems (2007, unknown): “Reiher’s result that s(Cp ⊕ Cp) = 4p − 3 (see [35] and [30, Theorem 5.”