Szalkai, István and Tuza, Zsolt (2015) Minimum number of affine simplexes of given dimension. DISCRETE APPLIED MATHEMATICS, 180. pp. 141-149. ISSN 0166-218X
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Abstract
In this paper we formulate and solve extremal problems in the Euclidean space Rd and further in hypergraphs, originating from problems in stoichiometry and elementary linear algebra. The notion of affine simplex is the bridge between the original problems and the presented extremal theorem on set systems. As a sample corollary, it follows that if no triple is collinear in a set S of n points in R3, then S contains at least fenced(frac(n, 4)) - c n3 affine simplices for some constant c. A function related to Sperner's Theorem and its well-known extension to reciprocal sums is also considered and its relation to Turán's hypergraph problems is discussed. © 2014 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | stoichiometry; Minimal linear dependency; Linear hypergraph; Extremal set theory; Euclidean affine simplex |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 17 Feb 2016 11:28 |
| Last Modified: | 17 Feb 2016 11:28 |
| URI: | http://real.mtak.hu/id/eprint/33709 |
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