Peter Dukes - Dukes, P: Convexity and the Structure of Designs

Peter Dukes - Dukes, P: Convexity and the Structure of Designs

61,99 €

Suppose 10 triangles on six points cover each of the 15 pairs of points exactly twice. There cannot be two disjoint triangles among the ten. For otherwise, 9 crossing pairs need to be covered twice each, while each of the other 8 triangles affords at most two such crossing pairs....

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Produktbeschreibung

Suppose 10 triangles on six points cover each of the 15 pairs of points exactly twice. There cannot be two disjoint triangles among the ten. For otherwise, 9 crossing pairs need to be covered twice each, while each of the other 8 triangles affords at most two such crossing pairs. The basic example above illustrates the technique which is pursued. A combinatorial design is identified with a nonnegative integral solution to a certain matrix equation involving an inclusion matrix. Some elementary convex geometry is applied, resulting in the ''cone condition'' for designs. This powerful condition is shown to imply something resembling Delsarte''s inequalities, along with various other old and new results on the structure of block intersections in combinatorial designs. Many open problems and possible new directions are discussed as well.
Marke VDM
EAN 9783639117370
ISBN 978-3-639-11737-0
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