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A note on matroids and block designs

Published online by Cambridge University Press:  09 April 2009

R. A. Main  and
D. J. A. Welsh
R. A. Main
Affiliation:
Mathematical Institute, University of Oxford, Oxford, U. K.
D. J. A. Welsh
Affiliation:
Mathematical Institute, University of Oxford, Oxford, U. K.
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The close connection between certain types of matroids or combinatorial geometries and block designs is well known. The relationships previously discussed have centred on the loose analogy between the blocks of a design and the hyperplanesor flats ot the matroid or geometry. The matroids which arise in this way have had in the main a very tight regular structure. Here we show that theclass of matroids whose bases are the blocks of a design ismuch wider — indeed from Theorem 6 below we obatain a metroid in a canonical way from any balanced incomplete block design in which no pair of blocks differ by exactly one element.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 1 , August 1975 , pp. 54 - 58
Copyright
Copyright © Australian Mathematical Society 1975

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